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

Chapter 2 All Rights Reserved 1

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 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


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


Measuring Returns Holding Period Return Relative (HPRR) [Eq. 2-2]

1t

ttt P

CFPHPRR

HPR = HPRR - 1


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


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:

T / HPRARORT

1tt


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


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 HazardMoral 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)

2i

n

1ii 0,RERminxP


Measuring Risk Finance

Standard Deviation (SD)

1/2T

1t

2t AROR)(HPR

1T

1][ SD

n

1t

2

t2 RR

1n

1][σ Variance


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 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



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



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



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



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%



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

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

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