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Chapter 2Measuring Return and Risk

- Measuring Returns
- Measuring Risk
- Distributions

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

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

Returns on Investment

- Ex Ante Returns
- Returns derived from a probability distribution
- Based on expectations about future cash flows
- 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

Measuring Returns

- 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

Measuring Returns

- Holding Period Return Relative (HPRR) Eq. 2-2

- HPR HPRR - 1

Measuring Returns

- Per-Period Return (PPR) Eq. 2-3
- Return earned for particular period (for example,

annual return) - Per-Period Return (Periods Income Price

Change) ? Beginning Period Value - Per-Period Return Relative (PPRR) Eq. 2-3a
- Per-Period Return Relative (Periods Income

End of Period Value) ? Beginning Period Value - PPR PPRR - 1

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

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

Measuring Average Returns

- Average Rate of Return (AROR) as Arithmetic

Average

Measuring Geometric Returns

- Geometric Returns as Product (P)

GHPR as a mean geometric holding period

return Arithmetic Average Returns upwardly biased

Expected Returns

- Probability Distributions
- Normal
- Leptokurtic
- Platykurtic
- Skewed
- Expected Returns are State of Nature specific

probability assignments

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

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

Types of Risk

- Pure Risk
- Involves only chance of loss or no loss
- Casualty insurance is a good example
- Moral Hazard Problem
- Adverse Selection
- Speculative Risk
- Associated with speculation in which there is

some chance of gain and some chance of loss

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

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

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)

Measuring Risk

- Finance
- Standard Deviation (SD)

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.

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)

Investment Leverage Buying on Margin

- Buying on Margin
- Margin rate percentage of securities purchase

that must come from investors 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

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

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

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

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

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

Take-Home Exercise

- Mini-case starting page 2.54