Portfolio Management

							    Portfolio Management

CHAPTER 13
Revision of the Equity
Portfolio
                      Key Terms
•   Passive management        •   Dollar cost averaging
•   Active management         •   Floor value
•   Buy and hold              •   Indexing
•   Churning                  •   Multiplier
•   Constant beta portfolio   •   Naïve strategy
•   Constant mix strategy     •   Rebalancing
•   Constant proportion       •   Tracking error
•   Portfolio insurance       •   Closet indexing
•   Crawling stop
•   Asset class appraisal
•   churning
       Portfolio Management

• Construct according to investment policy
• Monitor performance
  – Relative to a benchmark
  – Total return
• Revision according to investment policy
• Evaluate performance
                                    This is the focus of
  – Attribution of returns             this chapter.
     Portfolio Revision Strategies
 Balanced Funds (Debt and              All Equity Portfolios
           Equity)

• Constant Mix (static strategy)   • Constant proportion
• Constant Proportion Portfolio    • Constant beta
  Insurance (reactive strategy)
• Tactical Asset Allocation
  (anticipatory strategy)
        Building Equity Portfolios

• Active (market timing versus stock picking)
  versus Passive Approaches (indexing through
  full replication, sampling or quadratic
  optimization techniques)
• Top-Down (tactical/strategic asset allocation)
  versus the Bottom-up (stock-picking) Approaches
• Management Styles: value versus growth
  investing
           Passive Management
• Passive equity portfolio management is a long-term buy
  and hold strategy.
• Usually stocks are purchased so the portfolio’s returns will
  track those of an index over time….because of the goal of
  tracking an index, this approach to investing is generally
  referred to as “indexing.”
• Occasional rebalancing is required since dividends must be
  reinvested and because stocks merge or drop out of the
  target index and other stocks are added.
• Notably, the purpose of an indexed portfolio is not to
  “beat” the target index, but to match it’s performance.
        Passive Management …
• A manager of an equity index portfolio is judged on how
  well he or she tracks the target index – that is, minimizes
  the deviation between portfolio and index returns (ie.
  tracking error) similar to the bond index portfolio manager.
• Measurement of performance of an index fund manager
  can be done through regression analysis…regress the
  returns of the portfolio against the returns of the target
  index. The beta of such a portfolio should be close to 1
  and the R2 should be high and the alpha should be close to
  0. The closer these regression statistics are to these target
  values, the better the index fund manager’s performance.
              Passive Management
• The goal of a passive portfolio is to match the returns to the index as
  closely as possible.
• Generally, you would expect an index fund’s performance to lag the
  performance of the target index….why?
    – Because of cash inflows and outflows (assumes an open-ended fund where
      further units are sold and outstanding ones are redeemed) and company
      mergers and bankruptcies, securities must be bought and sold, which
      means that there inevitably will be differences between portfolio and
      benchmark returns over time.
    – In addition, even though index funds generally attempt to minimize
      turnover and the resultant transactions fees, they necessarily have to do
      some rebalancing, which means in the long-run return performance of
      index funds will lag the benchmark index.
• Certainly, substantial or prolonged deviations of the portfolio’s returns
  from the index’s returns would be a cause for concern.
           Passive Management

• Three basic techniques for constructing passive index
  portfolios:
   – Full replication
   – Sampling
   – Quadratic optimization
             Full Replication
• All securities in the index are purchased in
  proportion to their weights in the index.
  – Ensures close tracking
  – But may be sub-optimal because:
     • The need to buy many securities will increase
       transactions costs that will detract from performance
     • The reinvestment of dividends will also result in
       high commissions when many firms pay small
       dividends at different times in the year
                   Sampling

• Only a representative sample of the stocks that
  make up the index are purchased
• Tracking error (is the greatest disadvantage to this
  approach.)
• Full replication of the S&P 500 would (in theory)
  have almost no tracking error. As smaller samples
  are used to replicate the S&P performance, the
  potential tracking error increases.
   Sampling Technique to Building
         an Index Portfolio
Expected
Tracing
Error
(percent)
        4.0


        3.0


        2.0


        1.0




              500   400   300   200         100
                                      Number of Stocks
          Quadratic Optimization

• Rather than obtaining a sample based on industry or security
  characteristics, quadratic optimization or programming
  techniques can be used to construct a passive portfolio.
• With quadratic programming, historical information on price
  changes and correlations between securities are input to a
  computer program that determines the composition of a
  portfolio that will minimize tracking error with the benchmark.
• A problem with this technique is that it relies on historical price
  changes and correlations, and if these factors change over time,
  the portfolio may experience very large tracking errors.
              Completeness funds
• Some passive portfolios are not based on a published index.
• Sometimes customized passive portfolios, called completeness funds
  are constructed to complement active portfolios that do not cover the
  entire market.
• For example, a large pension fund may allocate some of its holdings to
  active managers expected to outperform the market. Many times these
  active portfolios are over-weighted in certain market sectors or stock
  types. In this case, the pension fund sponsor may want the remaining
  funds to be invested passively to “fill the holes” left vacant by the
  active managers.
• The performance of completeness funds will be compared to a
  customized benchmark that incorporates the characteristics of the
  stocks not covered by the active managers.
       Rebalancing Portfolios

• Constant mix strategy
  – Adjustments are made so as to maintain the
    relative weighting of the asset classes within
    the portfolio as their prices change
  – Implication:
     • Purchase securities that have performed poorly and
       sell those that have performed the best.
         Rebalancing Portfolios

• Constant proportion portfolio insurance

   $ in stocks = Multiplier × (portfolio value – floor value)

   – CPPI strategy buys stock as it rises.
      • Does best in a rising market because the portfolio manager will
        be buying stock in a rising market which is logically a
        moneymaker.
      • If the market falls, CPPI will gradually revert to 100 percent
        bonds since stock is sold as the market falls.
     Other Rebalancing Issues
• Trading fees:
  – Commissions
  – Transfer taxes
• Management time
• Tax Implications
• Window Dressing
       Key Points in the Chapter

• An important point in this chapter is the distinction
  between active and passive management.
• Portfolios can be rebalanced in various ways. The constant
  beta, constant proportion, and constant proportion portfolio
  insurance methods illustrate common ways in which this
  might be done.
• Dollar cost averaging is a valuable investment technique
  for the individual. (see the slide set on this web site.)
                Question 13 - 1

• There is much to be said in favour of buy-and-hold
  strategies. Ideally, though, such a strategy is used on
  purpose rather than because of inattention. To the extent
  that most portfolios require the periodic reinvestment of
  dividend and interest income received, the statement is
  true: the portfolio will routinely be revised as cash
  accumulates. The portfolio also will periodically
  encounter mergers, tender offers, and rights offerings, and
  these also have portfolio revision overtones.
                 Question 13 - 2

• Someone who rebalances wants to maintain a portfolio
  with particular investment characteristics. Whether these
  characteristics are reasonable or not is another story.
• The empirical evidence also suggests that managers are not
  able consistently to time the market or earn a return greater
  than that associated with the security’s level of risk. In
  some respects, an active manager does not believe in the
  efficient market hypothesis.
               Question 13 - 3

• Commissions must be paid, there may be tax
  considerations, and it takes time.
                 Question 13 - 4

• A crawling stop provides protection (although incomplete
  protection in the event of a crash; a stop order activates a
  market order, and the market price may change quickly)
  against adverse price movements while leaving open the
  possibility of further gains.
• The stop price can be moved behind a rising stock to
  protect a progressively larger profit.
                Question 13 - 5

• Ignorance is the primary reason, and stockbrokers seem to
  forget to recommend them to their customers.
                 Question 13 - 6

• A correlation of .96 is very high. To move closer to 1.00
  would be expensive in terms of additional commissions,
  and probably is not necessary. Still, on a large portfolio, a
  failure to mimic the market as best as possible might result
  in unacceptably large deviations in the dollar value of the
  portfolio from the target value.
                 Question 15 - 7

• If a portfolio states its objective as capital appreciation, it
  should normally be an equity portfolio.
• A mutual fund with such an objective probably would not
  be able to convert completely to cash because of
  prospectus provisions. Market risk could, however, be
  reduced via derivative assets such as stock index futures or
  options.
                Question 13 - 8

• Probably not, although some people might feel that 15% is
  too far away from the current price.
                 Question 13 - 9

• This is a debatable point that is routinely argued in courts
  of law. An important factor is the manager’s performance;
  did the unusually high level of turnover result in gains to
  the customer or only commissions in the broker’s pocket?
               Question 13 - 10

• This is a restrictive covenant.
• A portfolio might be equally weighted or constant beta, but
  doing both is more technical. It can be done, but would be
  expensive in terms of the number of adjustments required.
               Question 13 - 11

• Most portfolios generate cash because of the receipt of
  dividends and the occasional tender offer. As the level of
  cash held increases, the portfolio beta declines because
  cash has a beta of zero and will water down the risk of the
  portfolio. If the market value of the equities continues to
  rise, however, this could offset an increase in the cash
  proportion.
               Question 13 - 12

• Security prices will fluctuate. If the market is efficient,
  though, they will show an appropriate expected return over
  long term. This means that they should be bought in a
  period when they perform poorer than their expected
  return, as they will (on average) make it up in a subsequent
  period. The converse holds true if they do unusually well.
                Problem 13 - 2

• The basic approach is to sell some stocks that have
  appreciated and buy more of those that have declined.
                 Problem 13 - 3

• Portfolio beta = 1.08 = weighted average of the betas of the
  various stocks that make up the portfolio:
                 Problem 13 - 3

• To bring the portfolio beta back to the target beta of 1.10
  could be done by selling low beta securities and buying
  more of the higher beta securities.
                 Problem 13 - 4

• Cash has a beta of zero. Therefore, selling a proportional
  amount of every portfolio asset and holding the proceeds in
  cash will reduce the beta proportionately, too.
• Solve for X in the following ratio:
                    Problem 13 - 5
• This is a market rise of 100/14000 = .71%.
• Each security should therefore rise by its beta multiplied by 0.71%
                 Problem 13 - 7

A.   Variance of A = 0.001660
     Variance of B = 0.000910
     (Note that the variance is of the returns, not of the share
     price).
B.   At the end of the period, 121.218 shares would have
     been accumulated in Fund A. Worth $12,76 apiece, this
     is a total value of $1,546.74. In Fund B, 122.17 shares
     would have been accumulated. At $13.08 apiece, this
     fund value is $1,597.98
                 Problem 13 - 8

• Contributions were made into the funds; if these are not
  considered, the apparent fund return will be substantially
  biased upward. A technique for dealing with this issue is
  discussed in Chapter 19 (Performance Evaluation).
  Viewed as a two-security portfolio with equal weighting,
  the return each month is the average of the two individual
  returns. This produces a portfolio return variance of
  0.001118.
                   Problem 13 - 9
• The value of the stocks is $117,380. Unless you know precisely when
  the dividends are paid you cannot calculate an exact answer. An
  approximate answer comes from the following logic.
                    Problem 13 - 9
• Note that this figure is approximately half the amount that would have
  been earned on 4% of the total portfolio value @ 6% for one year. The
  lower figure reflects the fact that, on average, the dividends are only
  invested half the year if the dividend payment dates are uniformly
  spread over the calendar year.
                   Problem 13 - 10

CFA Guideline Answer:
A. The primary characteristics of Constant Mix, Constant Proportion,
   and Buy and Hold strategies are related to changes in market values
   follow
    1. Constant Mix The constant mix strategy maintains a constant
       percentage exposure to all asset classes at all levels of wealth.
       The portfolio must be rebalanced to return to its target mix
       whenever asset values change significantly. Therefore, assets of
       one class are purchased when their value falls, while assets of
       another class are sold when their value rises. This strategy is
       typical of contrarian investors: More funds are put at risk in the
       asset class whose values have declined, which implies that the
                Problem 13 - 10 ...

CFA Guideline Answer:
A. The primary characteristics of Constant Mix, Constant Proportion,
   and Buy and Hold strategies are related to changes in market values
   follow
    1. Constant Mix … that the investors’ risk tolerance is constant.
       This “buy low, sell high” strategy supplies liquidity to the
       markets.
       Market environment for the best performance. The Constant
       Mix Strategy will provide the best relative performance when the
       capital markets are volatile and trendless (alternatively, choppy
       and featuring mean reversion).
               Problem 13 - 10 ...

2. Constant Proportion The Constant Proportion Strategy uses
   “portfolio insurance.” Fewer funds are left in the high-risk asset as
   wealth falls. A floor amount is established, which is invested entirely
   in low-risk (or risk-free) assets when the market value of the portfolio
   is equal to the amount of the floor. The remainder of the portfolio is
   invested in high-risk assets in some multiple of the difference
   between the floor amount and the market value of the total portfolio.
   Buying additional high-risk assets is required when their value
   increases (because portfolio value minus floor amount rises), whereas
   the sale of high-risk assets is required as their value falls. This
   liquidity-demanding, trend-following strategy buys the risky asset on
   strength and sells it on weakness.
               Problem 13 - 10 ...

2. Constant Proportion ...
       Market environment for the best performance. The Constant
       Proportion Strategy makes sense for investors whose risk tolerance
       is highly sensitive to changes in wealth. It provides the best
       relative performance when the markets are in a steady upward or
       downward trend.
    3. Buy and Hold. A Buy and Hold Strategy requires neither purchases nor
      sales once the original portfolio mix has been implemented. Such a
      strategy, given the absence of turnover, enjoys the advantage of avoiding
      postformation transaction costs, requires no “asset allocation
      management” (thereby avoiding management fees) and is blind to changes
      in market levels. Passive investors holding the market mix of
                Problem 13 - 10 ...

3. Buy and Hold. A Buy and Hold Strategy requires neither purchases
    nor sales once the original portfolio mix has been implemented. Such a
    strategy, given the absence of turnover, enjoys the advantage of
    avoiding postformation transaction costs, requires no “asset allocation
    management” (thereby avoiding management fees) and is blind to
    changes in market levels. Passive investors holding the market mix of
    of assets often use this strategy. The strategy implies that investors’
    risk tolerance increases as wealth increases.

    Market environment for best relative performance. The relative
    performance of the Buy and Hold Strategy will typically lie between
    that of the other two alternatives. It enjoys no “best” relative
                Problem 13 - 10 ...

3. Buy and Hold. ….
   Market environment for best relative performance. The relative
   performance of the Buy and Hold Strategy will typically lie between
   that of the other two alternatives. It enjoys no “best” relative
   performance environment but is a good strategy to follow over long
   periods in the United States, where the primary long-term trend has
   been upward.
B. Recommendation: Given the board’s concern about downside risk,
   the recommended policy would be the Constant Proportion Strategy,
   with the Buy and Hold as a second choice. The Constant Mix Strategy
   provides the best performance only if the capital markets are volatile
   and trendless. It provides less of what the board considers important,
                Problem 13 - 10 ...
B. Recommendation: Given the board’s concern about downside risk,
   the recommended policy would be the Constant Proportion Strategy,
   with the Buy and Hold as a second choice. The Constant Mix Strategy
   provides the best performance only if the capital markets are volatile
   and trendless. It provides less of what the board considers important,
   namely, downside protection, than either of the other two strategies.
    Justification: If opportunity exists to rebalance on a timely basis, the
    Constant Proportion (portfolio insurance) Strategy provides the best
    downside protection. If that assumption is not made, the Buy and Hold
    Strategy can be recommended. The Buy and Hold Strategy typically
    performs between the other two (which make opposite bets on the
    volatility and trend of the market) and will do well when markets
                Problem 13 - 10 ...
B. Justification: … volatility and trend of the market) and will do well
   when markets follow a long-term , generally upward trend. Because
   the Buy and Hold Strategy is a relatively costless strategy to operate,
   the absence of turnover will positively affect the results over time.

    A secondary reason for considering the Constant Proportion Strategy is
    that its popularity has waned since the 1987 stock market crash, when
    the required transactions could not be affected in a timely manner. It
    may offer a mispricing benefit because of the supply/demand
    imbalance relative to the Constant Mix Strategy (a portfolio insurance
    seller).