Transcript Document 7314902

Chapter 2
Measuring Return and Risk
Measuring Returns
Measuring Risk
Distributions
Chapter 2
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Learning Objectives
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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
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Sources of Investment returns
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Dividends, Interest
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Capital gains/losses (Realized vs. Paper)
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Cash dividends on common, preferred stock
Interest (coupons) on Bills and Bonds
Increases/decreases in price
Other
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Chapter 2
Stock Dividends
Rights and Warrants
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Returns on Investment
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Ex Ante Returns
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Ex Post Returns
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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
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Measuring Returns
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Holding Period Returns (HPR) [Eq. 2-1]
Pt  Pt 1  CFt
HPR t 
Pt 1
Where: Pt = current price
Pt-1 = purchase price
CFt = cash flow received in time t
HPR normally computed on monthly basis
Chapter 2
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Measuring Returns
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Holding Period Return Relative (HPRR) [Eq. 2-2]
Pt  CFt
HPRR t 
Pt 1
 HPR = HPRR - 1
Chapter 2
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Measuring Returns
 Per-Period Return (PPR) [Eq. 2-3]
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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
Chapter 2
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Compounding
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Computing Future Values given a ROR
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FV = Begin Value * (1 + ROR)t [Eq. 2-4]
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Example: What is the future value of $10,000
invested for 10 years if the ROR is 8%?
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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
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Compounding
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Computing the Effective Annual Rate
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Rear = (1 + HPR)12/n
-1
Example: You realize a 6.5% return over a 4
month period. What is the EAR
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Chapter 2
(1.065)12/4 - 1 = 0.2079 = 20.79 % per annum
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Measuring Average Returns
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Average Rate of Return (AROR) as
Arithmetic Average:
T
AROR   HPR t / T
t 1
Chapter 2
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Measuring Geometric Returns
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Geometric Returns as Product (P)*
T
GHPR  Π (1  HPR t )
1/T
1
t 1
*GHPR as a mean geometric holding period return
Arithmetic Average Returns upwardly biased
Chapter 2
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Expected Returns
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Probability Distributions
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Normal
Leptokurtic
Platykurtic
Skewed
Expected Returns are State of Nature
specific – probability assignments
Chapter 2
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Portfolio Expected Returns
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Weighted Average Rate of Return
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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
Chapter 2
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Risk and return:
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What is risk?
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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
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Types of Risk
 Pure Risk
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Involves only chance of loss or no loss
Casualty insurance is a good example
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Moral Hazard Problem
Adverse Selection
 Speculative Risk
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Chapter 2
Associated with speculation in which there is
some chance of gain and some chance of loss
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Sources of Risk
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Investment Theory: Market Risk
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Purchasing Power – impact of inflation
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Diversifiable vs. Non-Diversifiable (CAPM)
Real vs. Nominal Returns
Interest Rate Risk
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Chapter 2
Changes in market values when rates change
Price risk vs. Reinvestment Rate Risk
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Sources of Investment Risk
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Business Risk (non-systematic)
Financial Risk
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Default, Liquidity, Marketability, Leverage
Exchange Rate Risk – Political Risk
Tax Risk (changes in code, treatment)
Investment Manager Risk
Additional Commitment Risk
Chapter 2
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Measures of Risk
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Standard Deviation
Coefficient of Variation CV = SD / Mean
Beta (CAPM – relative risk – market)
Range: highest to lowest expected values
Semi-Variance (trimmed mean)
n
 Pi xmin R i  ER ,0
2
i 1
Chapter 2
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Measuring Risk
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Finance
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Standard Deviation (SD)
1/2
 1
2
SD [ ]  
(HPR t  AROR) 
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 T  1 t 1
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T
n
1
2
2
R t  R 
Variance [σ ] 

n  1 t 1
Chapter 2
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Risk and Return
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Fundamental Relationship
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Investors assumed to be risk averse:
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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
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Monte Carlo Simulation
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Dealing with random nature of returns
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Use of random numbers (probabilities) to vary
expected future outcomes.
Computer programs will generate numbers
between 0 and 1. Output range can be set:
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Chapter 2
Example: only values between 0 and .25
Random effects may be positive or negative
(requires two draws)
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Investment Leverage – Buying on
Margin
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Buying on Margin
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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
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Investment Leverage – Buying on
Margin
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Margin Rates
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Federal Reserve Board vs. In-house rule
Regulation T
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NYSE's Rule 431 & FINRA's Rule 2520
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Chapter 2
50% initial margin rate
25% maintenance margin rate [MMR]
30% on short positions
In-house requirements may be higher, never lower
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Investment Leverage – Buying on
Margin
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Buying Power
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Dollar value of additional securities that can be
purchased on margin with current equity in
margin account
BP a function of Net Equity position
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Chapter 2
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
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Margin Calls
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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
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Chapter 2
Deposit (or transfer additional funds)
Liquidate a portion of portfolio – proceeds to pay down
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Investment Leverage – Buying on
Margin
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Effects of Margin Buying on Investment
Returns
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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%
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Investment Leverage – Buying on
Margin
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Broker Call-Loan Rate
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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
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Take-Home Exercise
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Mini-case starting page 2.54
Chapter 2
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