Mathematics and Interest Rate Risk Management

Free Pizza (but not a free lunch) Mathematics and Interest Rate Risk Management Why choose mathematics?  A challenging, yet rewarding set of material. Mathematics can be used to explain or model many situations in the physical and social sciences.  Problems of interest    If I walk halfway to a wall, and then walk halfway to the wall from that point, and then continue on with this process, how many steps will it take me to reach the wall? For any integer n, if I take n steps, there will be some positive distance to the wall. Taking infinitely many steps, however, will allow one to have moved the entire distance to the wall Problems of interest Line segments and size  Which is bigger? A: _______ or B: _________________  Answer: Depends on how you are measuring.  Educational experience  Mathematics, Economics, and Business (Finance) at BWC, along with Mathematics at Miami of Ohio.  While at BWC, my understanding of mathematics helped me gain a deeper understanding of subjects such as economics and finance. Economics  Increased exposure to mathematics will improve your computational skills, which are certainly important in an economics setting.  Mathematics also helps one understand economic concepts. Economics  Profit maximization Why MR=MC? Profit = Revenue – Cost    Calculus can help us maximize profit Economics and Statistics  Econometrics is an important area of economics  Understanding the fundamental concepts of statistics may help lead to a better understanding of econometric techniques Finance  Geometric Series (Walking halfway to the wall, and again, and again, …) Dividend Growth Valuation Model: –  Value of a stock is based on the required rate of return, the dividend, and the dividend growth rate. Finance  Modern Portfolio Theory – How do I assemble a collection of assets with optimal risk and return characteristics?  Diversification – Risk reduction by selecting assets with a correlation of less than one.  Bond math: Duration and Convexity (Calculus) Finance     Option and Other Derivative Pricing Very math intensive to derive the formula Yield curve analytics can be very math intensive as well. Aren’t all the formulas figured out already? – For the most part, yes, but understanding the derivation of the formula can provide great insight. Interest Rate Risk  What is interest rate risk? – Changes in value of instruments or income due to movements in market rates.  Example: Treasury Bond – If I own a 10 year Treasury Bond with a coupon of 4%, and market rates increase, what happens to the value of my bond? IRR Management  Some Types of Interest Rate Risk – – – Repricing Risk Option Risk Basis Risk Reprice Risk  Example – 5 year fixed rate asset funded with floating rate debt which has a monthly rate reset. If interest rates decline, a benefit is received. If interest rates rise, a detriment is incurred. – – Option Risk  Example: Mortgage Prepayment – If mortgage rates fall, homeowners may have an incentive to refinance their current mortgage to one with a lower interest rate. Basis Risk  Example: 3 month LIBOR loan funded with 3 month T-Bill debt. – If 3 month LIBOR and 3 month T-Bill rates do not move the same amounts through time, the effects of basis risk can be felt. Some methods to measure risk overall  Income Simulation – Measure sensitivity of Net Interest Income to different market interest rate scenarions  Valuation approach – Similarly, measure sensitivity of value to interest rate movements Other Areas of Finance  Behavioral Analysis Other areas of financial risk management. Insurance: actuarial modeling    Questions?