THE JOURNAL OF PORTFOLIO MANAGEMENT by RyanWinterswyk

VIEWS: 108 PAGES: 8

									                 nterpreting the Evidence on
                Risk and Expected Return:                     A


                Comment
                Robert A. Haugen and Nardin L. Baker




                                                                               n his article, “The Eftilsient Index and Prediction


                                                                          I    of Portfolio Variance,” Kenneth Winston 119931
                                                                               attempts to make two points:

                                                                         1. If you desire to move wzst (toward lower variance)
                                                                            on a mean-variance mapping, there may be equal-
                                                                            ly effective ways of accomplishing this other than
                                                                            by simply investing in those portfolios with Lowest
                                                                            past volatility.
                                                                         2. The superior performance of low-volatility port-
                                                                            folios isn’t significant given the ambiguity associat-
                                                                            ed with changing the constraints imposed on the
                                                                            optimization.

                                                                                We have always agreed completely with the first
                                                                         point. Optimization based cn factor models makes use
                                                                         of fundamental data, more observations, and contem-
                                                                         porary values for portfolio factor exposures. It would
                                                                         be surprising if there were no useful information in
                                                                         the additional information these models provide.
                                                                                Our objective [1991] was not to find the most
                R O B E R T A. H A U G E N is a                          accurate procedure to estimate future portfolio volatili-
                Professor at the Graduate School of                      ty. Rather it was to document the relative performance
                Management at the University of                          of portfolios that had relatively low volatility relative to
                California at Irvine (CA 92717).                         capitalization-weighted market indexes. As it turns
                                                                         out, the low-volatility portfolios of the past depend-
                NARDIN L. BAKER is Director                              ably produce subsequent low volatility.
                of Research at National Investment                              Our test exploits this fact, just as Fama and
                Services of America in Milwaukee                         MacBeth [1974], Fama and French [1992], and
                (WI 53202).                                              numerous other studies have exploited the dependable

36   INTERPRETING THE EVIDENCE O N RISK A N D EXPECTED KETURN: COMMENT                                                     SPRING 1993
EXHIBIT 1                                                                                          PANEL C
FAMA/FR.ENCH STUDY         FIGURES 1A-1J
                                                                                                         .
                                                                                                        19
NEW YORK STOCK EXCHANGE, AMEX, AND
NASDAQ STOCKS (JULY 3963-DECEMBER 1990)




                                                                                                        ,1
                                                                                                         .
                                                                                                        11


PANEL A
     L9
      .
     10
     17
      .
      .
     16
                                                                                                        ,:I.,
                                                                                                        00
                                                                                                         .




                                                                                                        0.5
                                                                                                              05   06
                                                                                                                    .
                                                                                                                        ,   .
                                                                                                                            07
                                                                                                                             .
                                                                                                                                 . ,

                                                                                                                                  00
                                                                                                                                   .
                                                                                                                                        ,

                                                                                                                                         .
                                                                                                                                        09
                                                                                                                                              ,
                                                                                                                                                  Sire Dedle Three


                                                                                                                                                  ,

                                                                                                                                                  10
                                                                                                                                                       . ,

                                                                                                                                                         .
                                                                                                                                                        11
                                                                                                                                                              ,   ,

                                                                                                                                                                  L2
                                                                                                                                                                       .   ,


                                                                                                                                                                           13
                                                                                                                                                                                ,   ,

                                                                                                                                                                                    14
                                                                                                                                                                                     .
                                                                                                                                                                                          ,   ,

                                                                                                                                                                                              15
                                                                                                                                                                                               .
                                                                                                                                                                                                    .
                                                                                                                                                                                                     .
                                                                                                                                                                                                    16
                                                                                                                                                                                                          ,   ,

                                                                                                                                                                                                              L7
                                                                                                                                                                                                                    ,


                                                                                                                                                                                                                     .
                                                                                                                                                                                                                    10
                                                                                                                                                                                                                         ,   ~




                                                                                                                                                                                                                              .
                                                                                                                                                                                                                             19

     L5                                                                                                                                 Systemrtic Risk W e t Beta1
      .
     14
     L3
     13
      .
     11
                                                                                                   PANEL D
     LO
                                      Size Derile One
      .
     09
                                                                                                        19
      .
     08

     0.7

      .
     06
     0.5    1
           05
                .
                06
                 .
                     .
                     07
                      .
                          ,
                           .
                          00
                               . . .
                               a9    .
                                    10     .
                                          11
                                                I

                                               12
                                                        r

                                                         .
                                                        13
                                                              I


                                                             14
                                                              .   .
                                                                  l
                                                                   I


                                                                   5
                                                                       .   8


                                                                           16
                                                                            .
                                                                                I

                                                                                 .
                                                                                17
                                                                                     .    -

                                                                                         10
                                                                                          .
                                                                                              -

                                                                                               .
                                                                                              19
                                                                                                        1.6
                                                                                                                                                              *
                                                                                                        1.51
                                                                                                    E
                               Systematic Risk (Mprket Beta                                         E
                                                                                                   2
                                                                                                   P
                                                                                                   .Y
                                                                                                    2

                                                                                                    $   Lol
                                                                                                        a9
                                                                                                        00
                                                                                                         .    -                                    S i z e Dedle Fom
                                                                                                        0.7-
                                                                                                         .'
                                                                                                        06
PANEL B
                                                r
      L9




      1.6
                                                                                                   PANEL E

                                                                                                          .
                                                                                                         19


                                                                                                         1.7




                                                                                                         i.-----
                                Systematic R1sk (Market Beta)




                                                                                                         0.605
                                                                                                         0.5        .
                                                                                                                   06       07
                                                                                                                             .      .
                                                                                                                                   08     .
                                                                                                                                         09       10
                                                                                                                                                   .     11       l2       13        IA        15
                                                                                                                                                                                                .    L6        L7    10
                                                                                                                                                                                                                      .          19




                                                                                                                                        Systematic Risk (Market Bctd




 SPRING 1993                                                                                                                                 THE JOURNAL OF PORTFOLIO MANAGEMENT                                             37
   EXHIBIT 1                                                                                                                                      PANEL I
   CONTINUED
                                                                                                                                                       L9   -
   PANIlL F                                                                                                                                            1.8.

                                                                                                                                                       1.7.

          1.9-                                                                                                                                         1.6-
                                                                                                                                                       1.5-                   Size necile N i n e
          1.11.

         l.:?.                                                                                                                                     B   .4
                                                                                                                                                       l.

         1.G.
         1.:;-




                                                      Size Deeile Six
         0.7
                                                                                                                                                                      Systematic Risk (Market Beta)
         0.6

         0.54
            0.5
                        .
                       0.6
                              .
                             0.7
                                     .
                                    0.8
                                           .
                                          0.9
                                                 . . . . , .
                                                1.0      L1     U
                                                                         I

                                                                        13
                                                                              .   ,

                                                                                  L4
                                                                                        .    I

                                                                                            15
                                                                                                     .     I

                                                                                                          16
                                                                                                                .    ,

                                                                                                                    1.7
                                                                                                                          I   I

                                                                                                                              1.8
                                                                                                                                    .       ,

                                                                                                                                            1.9
                                                                                                                                                  PANEL J
                                          Systematic Risk (Market Beta



   PANEL G




                                                                                                                                                                                Sire Decile Ten

         1.5   j
         1.4 '

         1.3 '
         1.2

         1.1-
         1.0-

         0.9'



                              S i r e Decile Seven
                                                                                                                                                                      Systematic Risk (Market Beta)

         O . i J . . . . .. .. ......
             05.         0.6   0.7
                                     I


                                     08
                                      .
                                           .
                                          0.9
                                                 9

                                                1.0
                                                          I " " I " " I " ' ~ I " ~ ' I

                                                         1.1    12      1.3       L4        1.5
                                                                                                 ---'a"
                                                                                                          1.6       l.7       1.8
                                                                                                                                    ' " 1
                                                                                                                                            1.9

                                          Systematic Rirk (MarketBeta)




   PANEL H                                                                                                                                        relationship between historic beta subsequent beta in
                                                                                                                                                  order to conduct their tests. It would seem foolish to
                                                                                                                                                  fault these studies for failing to use the "best" predic-
                                                                                                                                                  tors of future beta (such as the Barra model) in assem-
                                                                                                                                                  bling their test portfolios. They, as we, used procedures
                                                                                                                                                  that are straightforward and replicable.
                                                                                                                                                          Turning now to Winston's second point, we
         1.2'
                                                                                                                                                  find that over long periods of time (1971-1991) port-
                                                                                                                                                  folios with low volatility cf return produce higher
         1.1.

         LO.
                   n

                                                                                                                                    -             returns; moreover, this is true for nearly all three-year
         0.9.
                                                                                                                                                  windows within this overall period.
                                                Sire Decile E i a t
                                                                                                                                                          These results are confirmed by Winston [I9931

: : :    0.6-

         a5O S         0.6   0.7    0.8   0.9   O
                                                L        1.1    13      13        1.4       L5            l.6       1.7       IS            1.9
                                                                                                                                                  in his Figure 1, by Vange1isl:i [1992], and, as it turns
                                                                                                                                                  out, by the widely cited article by Fama and French
                                          Systematic Risk (Market Beta)                                                                           [1992]. Exhibit 1 reproduces ten graphs taken from

   38   INTERPRETING THE EVIDENCE O N RISK AND EXPECTED RETURN COMMENT                                                                                                                                SPRING 1'293
Table 1 of the Fama-French article. In each graph beta        EXHIBIT 2
is plotted horizontally and average realized monthly                   PoRTFoL1oS
                                                              DIFFERENT POPULATIONS
return vertically.
                                                                                                               RUSSELL 1wO
        Each graph represents a different size decile,             D.W%                                                 -
                                                                                                                (1579 1990)

going from small to large. The portfolios in each graph
are equally weighted and grouped in accord with their              17.W%]                '4 '7                EFFICIENT




pre-ranking betas computed in the previous twenty-                 1600%.

four to sixty months (depending on data availability).
 Lines of best fit are passed through the data in each of     2
                                                              B
                                                                   15.WR-


 the graphs. In all ten cases the lines have negative         $    II.MI%-

 slopes.
                                                                   U.00%        -
         Moving to a test of our own, the triangles plot-
 ted in Exhibit 2 show the performance of the Russell              12009.       -
 1000 stock index (largest 1,000 stocks), the Russell
                                                                   11.00%       -
 1000 Price Driven Index (half the capitalization of the
 1,000, with stocks having the higher ratios of market             10.00%4
                                                                            12.00%      14.00%      16.00%            18.00%         20.00%       2200%     24.00%
 price-to-book value ratios), and the Russell 1000                                                VOLATILITY OF QUARTERLY RETURN
 Earnings Growth Index (the other half of the total
 capitalization, with the stocks with the smaller book-
 to-price ratios). All three indexes are capitalization-
 weighted.                                                           Winston discounts results such as these because
         The time period covers the full history of the       of their sensitivity to weighting constraints (the
 Russell indexes allowing for a two-year initial estima-      constraints of the Efficient Index in the case of our
 tion period. The data used to construct Exhibit 2            results and those of Vangelisti, and equal-weighting
 encompass approximately 6,000 stocks from the New            constraints in the case of Fama and French). We
 York and the American Exchanges as well as the over-         believe, however, that these results should be taken
 the-counter market. The data base has been carefully         seriously. To make our case, we first show that
 cleaned for survival bias, and the actual history of the     Winston's tests of the constraint sensitivity should be
 stocks in each index has been used for portfolio
 construction.
         The circles show the subsequent performance
 of minimum-volatility portfolios built from each of the      EXHIBIT 3
 three Russell populations. At the beginning of each          EFFICIENT PORTFOLIOS FROM
 quarter we find the portfolio with the lowest trailing       DIFFERENT POPULATIONS
 twenty-four month volatility in accord with the Effi-
 cient Index weighting constraints. Note that in each of
 the three cases, a pure attempt to move west in the
 diagram results in a drift to the northwest.
         The squares show the out-of-sample perfor-                 0.15-


 mance of maximum-volatility portfolios, where at the
 beginning of each quarter, volatility is maximized over      5     0.14-


 the preceding twenty-four months, again subject to           E
                                                                    0.u-
 the constraints imposed on the efficient index. Note
 that, again, an attempt to move east results in a drift to         0.12-

 the southeast.
         Exhibit 3 shows the results of an identical                0.11.


 experiment on the Russell 2000 stock index (smallest
                                                                            .
stocks). Again, in attempting to move west we drift                  ILOOl           17.Wl       19.W        21.DDl         23.003       25.00%     27.0m

north, and in attempting to move east we drift south.                                        VOJATILITI OF QUARTERLYRETURN



SPRING 1993                                                                                       THE JOURNAL OF PORTFOLIO MANAGEMENT                         39
 heavily discounted, and then we attempt to provide a ly portfolios and finds that, while both portfolios
 convincing explanation of the results of Exhibits 1 outperform the S&P 500, there is a spread in their
 through 3.                                                 performance of 157 basis points.
                                                                    It should be obvious that without peifect omni-
 SENSITIVITY OF RESULTS TO                                  science, the probability of actually experiencing such
 OPTIMIZATION CONSTRAINTS                                   ambiguity in performance is infinitesimally small. If
                                                            one knows the future, an clptimization system would,
        In Exhibit 4 we plot the volatility of return over of course, be unnecessary.
an immediately preceding twenty-four-month period                   Undaunted, Winston relaxes the constraint
on the horizontal axis and realized return over the further and examines all portfolios having the same
next quarter on the vertical axis. Two minimum-vari- variance as those between IC           and D. These portfolios
ance sets are pictured in the graph. One shows the are in the range A to F in Exhibit 4. A subset 0-’ these
portfolios with lowest possible variance in the previous (perhaps in the range B to E) will have exactly the
twenty-four months, given their return in the next same sequence of (or as in his second test similar)
quarter, assuming a weight constraint equal to three returns as those between C and D. Agzin, a t the
times the stock’s capitalization weight. The other beginning of each quarter, Winston finds the portfolio
shows the minimum-variance set with a less binding (B) with the highest subsequent quarterly return (H)
constraint of four times.                                   and the portfolio (E) with the lowest subsequent
        Considering the three times set first, Winston return (K) and again links the sixty quarterly returns.
alleges that for his test the nose of the minimum-vari-             What is this test supposed to show? Since, in
ance set has a flat portion ranging from C to D, all any given quarter, differen: stock portfolios produce
having the same sequence of twenty-four past monthly heterogeneous returns, the minimum-variance sets like
returns. At the beginning of each subsequent quarter those of Exhibit 3 will typically prove to be wide
from 12/75 to 12/90, he finds the portfolio (C) that rather than narrow. Given this, linking of the qu.irterly
produces the highest return in the next quarter (I) as extremes will naturally produce extremely different
well as the portfolio (D) that produces the very lowest linked returns. Yet this tells 11s nothing about the prob-
return 0).He then links the sixty quarterly returns of ability of actually experiencing ambiguity in perfor-
the hghest quarterly portfolios and the lowest quarter- mance when changing the constraints imposed on the
                                                           optimization.
                                                                    To determine the extent to which our results
                                                           are constraint-induced, we need to examine the simi-
EXHIBIT 4                                                  larity in performance of portfolios like M (a solution
MINIMUM-VARIANCE SETS                                      portfolio under a three times constraint) with portfo-
FOR fILTERNATE CONSTRAINTS                                 lios like M’ (a solution portfolio under a four times
                                                           constraint). We show such comparisons in Exhibit 5.
                                                                   Exhibit 5 shows the quarterly performance of
                                                           minimum-volatility portfc lios (estimated from the
                                                           twenty-four months of returns preceding each quarter)
                                                           optimized under different constraints. “M” indicates
                                                           the multiple of the S&P 500 capitalization weight
                                                           allowed in the optimization; “T” indicates the level of
                                                           annual turnover experienced in constructing the port-
                                                           folios over the period 1972-1990. (The multiple is
                                                           held at 3.0 for the different portfolio turnovers.)
                                                                   Our performance lie; to the northwest of the
                                                           S&P 500 under all these Constraint specifications. As
                                                           the results presented abovlz clearly show, reducing
                                                           volatility tends to increase return, not because of the
                                                           nature of our constraints, hut rather because of the

40   INTE.RPRETING THE EVIDENCE ON RISK AND EXPECTED RETURN: COMMENT                                     SPRING 1993
nature of the terrain in the equity markets between             EXHIBIT 5
1972 through 1990 and much longer. (See Haugen and              CONSTRAINT SENSITIVITY 1972-1990
Heins [1975] for an examination of the relative perfor-
mance of high- and low-risk stock portfolios over the
period 1926 through 1972.)

WHY LOW RISK TENDS TO
BRING HIGH RETURN
IN THE EQUITY MARKET

       We now consider two possible explanations for
the results of Exhibits 1 through 3.

1. The relationship between risk and expected return
    is more complex than that predicted by the               2.00%  (111
    CAPM. This explanation is consistent with the
    existence of an informationally efficient capital
                                                             0.00%      I
                                                                       200%  4.00%   6Do%    8.00%  10.00%  1200% 14.002 1600%



    market.                                                                        VOLATILITY OF QUARTERLY RETURN


2. The world is more mean-reverting than investors
    believe it is. The market cross-sectionally overre-
    acts to lengthy records of abnormal growth in                  First, there is a great deal of evidence docu-
     earnings per share, pricing growth stocks too high menting the mean-reverting property of the growth in
    and their value counterparts too low. As it turns inhvidual earnings-per-share. Little [1962] pioneered a
     out, the overvalued growth stocks (which subse- lengthy list of studies in the finance and accounting
     quently produce low returns) are also character- journals showing that statistical models become impo-
    ized by high volatility in return, and the tent in forecasting the relative growth of an individual
    undervalued value stocks (which subsequently stock beyond a few quarters into the future, and
    produce high returns) have low volatility in return. professional analysts perform only slightly better than
     Thus, the misconception about mean-reversion the statistical models. (See, for example, O’Brien
     overshadows investor preferences relating to risk. [1988].) To be sure, all these tests have been performed
     (This explanation, of course, is consistent with an on individual stocks; the predictability of relative
     inefkient capital market.)                          growth in portfolios is likely to be better.
                                                                   However, the key question is whether the actu-
        Fama and French find the ratio of a stock’s al predictability is less than the assumption embedded
book value to market value is the best predictor of in the cross section of stock prices. There we see
future return. Their explanation (number 1 above) is widely varying ratios of market price to current cash
that stocks with high book-to-market are “fallen flow. To be sure, this variation may reflect either cross-
angels” - scary stocks with troubled records for sectional differences in risk premiums or market fore-
which investors require (arid subsequently get) higher casts of differential relative growth for prolonged
returns.                                                 periods into the future.
        The alternative explanation (number 2 above) is            Second, there is growing evidence relating to
that the market overreacts to the record, projecting the timing of the receipt of the “risk premiums” that
further trouble into the distant future, underestimating should trouble the advocates of explanation number 1.
the mean-reverting nature of business conditions. As Lakonishok, Ritter, and Chopra (LRC) [1993] show
these stocks subsequently revert to the mean in terms that the poor performers of the past subsequently do
of their growth, the overreaction is corrected, produc- well, and the good performers subsequently do poorly.
ing high returns.                                        This, taken alone, remains consistent with explanation
       H o w can we distinguish between the two number 1, although the timing of the subsequent
explanations in the evidence?                            performance doesn’t seem to be.

SPRING 1993                                                                            THE JOURNAL OF PORTFOLIO MANAGEMENT   41
EXHIBIT 6                                                                            Studies by French, Schwert, and Stambaugh [ 19871
THE RELATIONSHIP BETWEEN BETA AND
                                                                                     and Haugen, Talmor, and Ibrous [1991] docuw-ent a
 BOOK/h&WXKET FOR FAMA/FRENCH
 PORTFOLIOS FORMED ON PRE-RANKING BETA                                               strong negative (positive) price reaction by equities to
                                                                                     unexpected increases (decreases) in market volatility.
    0.9 ‘
                                                                                     The evidence in the longitudinal studies is consistent
                                                                                     with strong investor aversion to market price volatility.
                                                                                             Given this, how are we to interpret the results
    O -
     S
                                                                                     of Exhibit l ? Taken at face \due, these graphs indicate

 1  0.7-
                                                                                     that investors require the lowest returns fi-om stocks
                                                                                     that contribute the most to the volatility of the cap-
                                                                                     weighted NYSE index (as measured by their betas) and


     ”‘1
                                                                  Q                  the greatest returns from the stocks that contribute the
                                                                                     least to the volatility of this index. T h e apparent
   O S 4 ’ , ’ ,          .   .   .   I   .   I   .   1
                                                                                     inconsistency is reconciled, however, if it is the case
      0.6       0.8        1.0       1.2-      1.4        1.6       1.8              that preferences relating to risk are being overshad-
    The four por(foUos at the two extremes split Ihe bottom and top deeiles in half.
    Source: “The Crm-Section of Expected Stock Returns,,“. Fama and French, Journal
    of Finance, Spring 1992.
                                                                                     owed by misconceptions relating to the mean-rcvert-
                                                                                     ing properties of earnings per share.
                                                                                            Fourth, stocks with high ratios of market price-
          LRC show that the subsequent superior perfor- to-book values do not seem to be particularly sexy, at
mance of the losers of the past comes 1) in the three- least in terms of their market price behaviors. Exhibit
day window a t the subsequent announcements of 6, taken from Fama and French [1992], shows that
earnings per share, and 2) at the turn of the year. The market risk varies inversely with the ratio of book-to-
most simple explanation of (1) is that the niean-revert- market. The scary properties allegedly associated with
ing tendency in the numbers is catching the market by high book-to-price stocks are not manifest in price
surprise as the numbers are announced. Alternatively, behavior.
one can argue that risk dramatically increases at the                                       Whichever explanaticn (risk premiums or over-
time of the announcements, but then one would have reaction) you advocate, Exhibit 6 provides a convinc-
to argue why the increase in announcement uncertain- ing explanation for the results of Exhibits 1 through 3.
ty is dramatically greater for value stocks (the losers of Portfolios of high book-to-price stocks are less volatile.
the past) and lower for growth stocks (the winners).                                 Whether you support explanation number 1 or 2, you
          Even more troubling is (2). There is little or no should expect these stocks to produce higher future
evidence of a dramatic increase in risk that would returns.
induce the materialization of large risk premiums                                           As with any explanation rooted in the notion of
concentrated at the turn of the year. Advocates of market inefficiency, those who advocate explanation
corrections of overreactions have an easier time number 2 must explain why the inefficiency hasn’t
explaining the consistency of these results with the been corrected.
notion of an overreaction followed by a subsequent                                          Short-term, relativell, riskless arbitrage oppor-
return to equilibrium.                                                               tunities, as those that appear for fleeting periods o f
          As the year turns, a fresh evaluation period for time in the options markets, are undoubtedly correct-
the performance o f many professional money ed very quickly. Investors are far more reluctant,
managers begins. As the “gun is fired to start the race,” however, to take on risky arbitrage opportunities that
these relatively informed managers can be expected to yield benefits over periods of‘years rather than days.
move aggressively into stocks they perceive to be                                           The lion’s share of equity capital is controlled
mispriced. If this is true, a significant fraction of the by fiduciaries who are evaluated relative to key bench-
pressure to return to equilibrium will be exerted at the marks. The evaluation procen imposed on the fiducia-
turn of the year.                                                                    ries not only focuses attenticn on performance relative
          Third, there is an inconsistency in the cross- to the benchmarks, but also considerably shortens the
sectional and longitudinal empirical results that should investment horizon.
also trouble the advocates of explanation number 1.                                         Pension fund managers are far more concerned

42   INTERPRETING THE EVIDENCE ON RISK AND EXPECTED RETURN. COMMENT                                                               SPRING 1993
with how tightly their equity portfolios track the             REFERENCES
returns to the S&P 500 than they are with pure volatil-        Fama, E., and K. French. “The Cross-Section of Expected Stock
ity of equity returns. The news that equities with lower       Returns.”joonrrial of Finance, Spring 1992.
volatility can be expected to have higher returns may
                                                               Fama, E., and J. MacBeth. “Tests of A Multiperiod Two Parameter
be attractive, but moving to the west in mean-variance         Model.”_70urrralof Political Economy, May 1974.
space means accepting more S&P tracking error. This
agency problem acts as a barrier to the movement of            French, K., G. Schwert, and R. Stambaugh. “Expected Stock Returns
                                                               and Volatility.”joournal ofFiriancial Economics, 1987, p. 3.
significant amounts of capital to take advantage of the
long-term arbitrage opportunity that is apparently             Haugen, R . , and N . Baker. “The Efficient Market Inefficiency of
there.                                                         Capitalization-Weighted Stock Portfolios.” journal of PortfDlio Manage-
                                                               ment, Spring 1991.

SUMMARY                                                        Haugen, R., and A.J. Heins. “ k s k and the Rate of Return on Finan-
                                                               cial Assets: Some Old Wine in New Bottles.” journal of Finaricial aftd
                                                               Quantitative Analysis, December 1975.
         In his article Winston suggests that our results
should not be taken seriously. We have argued here             Haugen, R . , E. Talmor, and W . Torous. “The Effect of Volatility
that 1) it is Winston’s test that should not be taken          Changes on the Level of Stock Prices and Subsequent Returns.” j o n r -
                                                               nal ofFinance, July 1991.
seriously, 2) that the nature of our results has been
confirmed repeatedly in the results of others, and 3)          Lakonishok, J., J. Ritter, and N. Chopra. “Performance Measurement
that there are two competing hypotheses offered in the         Methodology and the Question of Whether Stocks Overreact.”_lonrnal
literature, both of which are capable o f explaining all the   of Financial Economics, forthcoming in 1993.
results.                                                       Little, I.M.D. “Higgledy-piggledy Growth.” Institute o Statistics,
                                                                                                                    f
         Stocks with high book-to-price have been              Oxford. November 1962.
shown to produce high returns subsequently. This may
                                                               O’Brien, P. “Analysts’ Forecasts as Earnings Expectation.” Journal .f
be true because they are scary or because investors            Accounting and Economics, January 1988.
underestimate the mean-reverting properties of growth
in earnings per share. Regardless, portfolios with high        Vangelisti, M. “Minimum Variance Strategies: D o They Work?”,
book-to-price also have low subsequent market risk;            BARRA Newsletter, January/February 1992.

this explains why low market risk is persistently associ-      Winston, K. “The Efficient Index and the Prediction of Portfolio
ated with high return.                                         Variance.” joiwnal of Portfolio Marlagemerit, Spring 1993.




SPRING 1993                                                                               THE JOURNAL O F PORTFOLIO MANAGEMENT     43

								
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