# Chapter 2 Measuring Return and Risk Measuring Returns

• Slides: 28

Chapter 2 Measuring Return and Risk Measuring Returns Measuring Risk Distributions Chapter 2 All Rights Reserved 1

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

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

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

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

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

Measuring Returns § Per-Period Return (PPR) [Eq. 2 -3] n n 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 -3 a] § Per-Period Return Relative = (Period’s Income + End of Period Value) Beginning Period Value § PPR = PPRR - 1 Chapter 2 All Rights Reserved 7

Compounding n Computing Future Values given a ROR n FV = Begin Value * (1 + ROR)t [Eq. 2 -4] n n n Example: What is the future value of \$10, 000 invested for 10 years if the ROR is 8%? n Chapter 2 Where: t = number of periods ROR = assumed Rate of Return (1 + ROR)t = Future Value Interest Factor (FVIF) FV is also termed Ending Value FV = 10, 000 * (1. 08)10 = \$21, 589. 25 All Rights Reserved 8

Compounding n Computing the Effective Annual Rate n n Rear = (1 + HPR)12/n -1 Example: You realize a 6. 5% return over a 4 month period. What is the EAR n Chapter 2 (1. 065)12/4 - 1 = 0. 2079 = 20. 79 % per annum All Rights Reserved 9

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

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

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

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

Risk and return: n What is risk? n n n Chapter 2 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 All Rights Reserved 14

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

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

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

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

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

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

Investment Leverage – Buying on Margin n n n Chapter 2 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 All Rights Reserved 22

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

Investment Leverage – Buying on Margin n Buying Power n n Dollar value of additional securities that can be purchased on margin with current equity in margin account BP a function of Net Equity position n Chapter 2 E = MV – Loan BP = (E / IMR) – MV See examples 1 and 2 on page 2. 44 -. 45 All Rights Reserved 24

Investment Leverage – Buying on Margin Calls n n n 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 n n Chapter 2 Deposit (or transfer additional funds) Liquidate a portion of portfolio – proceeds to pay down All Rights Reserved 25

Investment Leverage – Buying on Margin n Effects of Margin Buying on Investment Returns n n n Chapter 2 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% All Rights Reserved 26

Investment Leverage – Buying on Margin n Broker Call-Loan Rate n n Chapter 2 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 All Rights Reserved 27