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Chapter 2 All Rights Reserved 1
Chapter 2Measuring Return and Risk
Measuring Returns
Measuring Risk
Distributions
Chapter 2 All Rights Reserved 2
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
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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
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Returns on Investment Ex AnteEx Ante Returns
Returns derived from a probability distribution Based on expectations about future cash flows
Ex PostEx Post Returns Returns based on a time series of historical data
Investment decisions largely based on ex post analysis – modified by ex ante expectations
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Measuring Returns Holding Period Returns (HPR) [Eq. 2-1]
1t
t1ttt P
CFPPHPR
Where: Pt = current price
Pt-1 = purchase price
CFt = cash flow received in time tHPR normally computed on monthly basis
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Measuring Returns Holding Period Return Relative (HPRR) [Eq. 2-2]
1t
ttt P
CFPHPRR
HPR = HPRR - 1
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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
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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
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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
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Measuring Average Returns Average Rate of Return (AROR) as
Arithmetic Average:
T / HPRARORT
1tt
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Measuring Geometric Returns Geometric Returns as Product ()*
1)HPR(1GHPR 1/Tt
T
1tΠ
*GHPR as a mean geometric holding period return
Arithmetic Average Returns upwardly biased
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Expected Returns Probability Distributions
Normal Leptokurtic Platykurtic Skewed
Expected Returns are State of Nature specific – probability assignments
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Portfolio Expected Returns Weighted Average Rate of Return
WARR = W1 x E(R1) + W2 x E(R2) + . . . + Wn x E(Rn)
where Wi = % of portfolio invested in security i
E(Ri) = expected per-period return for security i
Subject to: W1 + … + Wn = 1
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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
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Types of Risk Pure Risk
Involves only chance of loss or no loss Casualty insurance is a good example
Moral HazardMoral Hazard Problem Adverse Selection
Speculative Risk Associated with speculation in which there is
some chance of gain and some chance of loss
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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
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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
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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)
2i
n
1ii 0,RERminxP
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Measuring Risk Finance
Standard Deviation (SD)
1/2T
1t
2t AROR)(HPR
1T
1][ SD
n
1t
2
t2 RR
1n
1][σ Variance
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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.
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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)
Chapter 2 All Rights Reserved 22
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
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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
Chapter 2 All Rights Reserved 24
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
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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
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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%
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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
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Take-Home Exercise Mini-case starting page 2.54
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