1. Chapter 2All Rights Reserved1 Chapter 2 Measuring Return and Risk Measuring Returns Measuring Risk Distributions

2. Chapter 2All Rights Reserved2 Learning Objectives Sources of Investment Returns Measures of Investment Returns Sources of Investment Risk Measures of Investment Risk Monte Carlo Simulation Investment Performance and Margin

3. Chapter 2All Rights Reserved3 Sources of Investment returns Dividends, Interest Cash dividends on common, preferred stock Interest (coupons) on Bills and Bonds Capital gains/losses (Realized vs. Paper) Increases/decreases in price Other Stock Dividends Rights and Warrants

4. Chapter 2All Rights Reserved4 Returns on Investment Ex Ante Ex Ante Returns Returns derived from a probability distribution Based on expectations about future cash flows Ex Post Ex Post Returns Returns based on a time series of historical data Investment decisions largely based on ex post analysis – modified by ex ante expectations

5. Chapter 2All Rights Reserved5 Measuring Returns Holding Period Returns (HPR) [Eq. 2-1] Where: P t = current price P t-1 = purchase price CF t = cash flow received in time t HPR normally computed on monthly basis

6. Chapter 2All Rights Reserved6 Measuring Returns Holding Period Return Relative (HPRR) [Eq. 2-2]  HPR = HPRR - 1

7. Chapter 2All Rights Reserved7 Measuring Returns  Per-Period Return (PPR) [Eq. 2-3] Return earned for particular period (for example, annual return) Per-Period Return = (Period’s Income + Price Change)  Beginning Period Value  Per-Period Return Relative (PPRR) [Eq. 2-3a]  Per-Period Return Relative = (Period’s Income + End of Period Value)  Beginning Period Value  PPR = PPRR - 1

8. Chapter 2All Rights Reserved8 Compounding Computing Future Values given a ROR FV = Begin Value * (1 + ROR) t [Eq. 2-4] Where: t = number of periods ROR = assumed Rate of Return (1 + ROR) t = Future Value Interest Factor (FVIF) FV is also termed Ending Value Example: What is the future value of $10,000 invested for 10 years if the ROR is 8%? FV = 10,000 * (1.08) 10 = $21,589.25

9. Chapter 2All Rights Reserved9 Compounding Computing the Effective Annual Rate Rear = (1 + HPR) 12/n -1 Example: You realize a 6.5% return over a 4 month period. What is the EAR (1.065) 12/4 - 1 = 0.2079 = 20.79 % per annum

10. Chapter 2All Rights Reserved10 Measuring Average Returns Average Rate of Return (AROR) as Arithmetic Average:

11. Chapter 2All Rights Reserved11 Measuring Geometric Returns Geometric Returns as Product (  )* *GHPR as a mean geometric holding period return Arithmetic Average Returns upwardly biased

12. Chapter 2All Rights Reserved12 Expected Returns Probability Distributions Normal Leptokurtic Platykurtic Skewed Expected Returns are State of Nature specific – probability assignments

13. Chapter 2All Rights Reserved13 Portfolio Expected Returns Weighted Average Rate of Return WARR = W 1 x E(R 1 ) + W 2 x E(R 2 ) +... + W n x E(R n )  where W i = % of portfolio invested in security i  E(R i ) = expected per-period return for security i  Subject to: W 1 + … + W n = 1

14. Chapter 2All Rights Reserved14 Risk and return: What is risk? Uncertainty - the possibility that the actual return may differ from the expected return Probability - the chance of something occurring Expected Returns - the sum of possible returns times the probability of each return

15. Chapter 2All Rights Reserved15 Types of Risk  Pure Risk Involves only chance of loss or no loss Casualty insurance is a good example Moral Hazard Moral Hazard Problem Adverse Selection  Speculative Risk Associated with speculation in which there is some chance of gain and some chance of loss

16. Chapter 2All Rights Reserved16 Sources of Risk Investment Theory: Market Risk Diversifiable vs. Non-Diversifiable (CAPM) Purchasing Power – impact of inflation Real vs. Nominal Returns Interest Rate Risk Changes in market values when rates change Price risk vs. Reinvestment Rate Risk

17. Chapter 2All Rights Reserved17 Sources of Investment Risk Business Risk (non-systematic) Financial Risk Default, Liquidity, Marketability, Leverage Exchange Rate Risk – Political Risk Tax Risk (changes in code, treatment) Investment Manager Risk Additional Commitment Risk

18. Chapter 2All Rights Reserved18 Measures of Risk Standard Deviation Coefficient of Variation CV = SD / Mean Beta (CAPM – relative risk – market) Range: highest to lowest expected values Semi-Variance (trimmed mean)

19. Chapter 2All Rights Reserved19 Measuring Risk Finance Standard Deviation (SD)

20. Chapter 2All Rights Reserved20 Risk and Return Fundamental Relationship The greater the risk, the greater the expected return (positively related) Investors assumed to be risk averse: The will want the same return with less risk. Assume greater risk only for greater returns. Risk and Return relationship varies over time.

21. Chapter 2All Rights Reserved21 Monte Carlo Simulation Dealing with random nature of returns Use of random numbers (probabilities) to vary expected future outcomes. Computer programs will generate numbers between 0 and 1. Output range can be set: Example: only values between 0 and.25 Random effects may be positive or negative (requires two draws)

22. Chapter 2All Rights Reserved22 Investment Leverage – Buying on Margin Buying on Margin Margin rate: percentage of securities purchase that must come from investor’s funds rather than from borrowing Initial margin rate: used when determining cash needed for new purchase Maintenance margin rate: used when determining if margin call is needed

23. Chapter 2All Rights Reserved23 Investment Leverage – Buying on Margin Margin Rates Federal Reserve Board vs. In-house rule Regulation T 50% initial margin rate NYSE's Rule 431 & FINRA's Rule 2520 25% maintenance margin rate [MMR] 30% on short positions In-house requirements may be higher, never lower

24. Chapter 2All Rights Reserved24 Investment Leverage – Buying on Margin Buying Power Dollar value of additional securities that can be purchased on margin with current equity in margin account BP a function of Net Equity position E = MV – Loan BP = (E / IMR) – MV See examples 1 and 2 on page 2.44-.45

25. Chapter 2All Rights Reserved25 Investment Leverage – Buying on Margin Margin Calls M/C Threshold = Loan Value / (1 – MMR) Example: MMR = 25%, Loan = $50,000 M/C T = 50,000 / (.75) = $66,667. If value of portfolio drops below $66,667 – broker calls for $$$: Cash Required = Loan – [MV*(1-MMR)] Meeting Margin calls Deposit (or transfer additional funds) Liquidate a portion of portfolio – proceeds to pay down

26. Chapter 2All Rights Reserved26 Investment Leverage – Buying on Margin Effects of Margin Buying on Investment Returns ROI = (Sell – Buy) / Buy ROI = (50000 – 40000) / 40000 = 25% 50% Margin: (50000 – 40000) / 20000 = 50% ROI = (50000 – 60000) / 60000 = - 16.66% ROI = (50000 – 60000) / 30000 = - 33.33%

27. Chapter 2All Rights Reserved27 Investment Leverage – Buying on Margin Broker Call-Loan Rate Interest rate charged by banks to brokers for loans that brokers use to support their margin loans to customers Usually scaled up for margin loan rate

28. Chapter 2All Rights Reserved28 Take-Home Exercise Mini-case starting page 2.54