Measuring

1
Chapter 2

• Measuring
• Returns and Risk

2
Measures of Investment Returns

• Holding Period Return (HPR) and Return Relative
  (HPRR)
• Per-Period Return (PPR) and Return Relative
  (PPRR)
• Compounding
• Expected Return
• Annualized Return
• Geometric Mean (GMR) and Arithmetic Mean Returns

3
Ex Ante Returns

• Returns that are derived from a probability
• distribution

Ex Post Returns

• Returns that come from a time series of
• historical data

4
Components of Return

• Periodic payments dividends, interest, rents, or
  royalties
• Changes in market value price appreciation or
  decline

5

• Holding Period Return (HPR)
• Rate of return for the period held
• Holding Period Return Relative (HPRR)
• End-period value relative to beginning-of-period
  value for specific holding period
• holding period return plus one (1)

6

• HPR (Income Received Change in Value) ?
  Beginning Value
• HPRR (Income Received Ending Value) ?
  Beginning Value
• HPR HPRR 1 or 1 HPR HPRR

7

• Per-Period Return (PPR)
• Return earned for particular period (for example,
  annual return)
• Per-Period Return (Periods Income
  Price Change) ? Beginning
  Period Value
• Per-Period Return Relative (PPRR)
• Per-Period Return Relative
• (Periods Income End of Period Value)
  ? Beginning Period Value

8
Impact of Compounding

• Ending Value Beginning Value x (1 rate of
  return)t
• where t the number of
  time periods
• Example
• beginning value 100
• rate of return 10
• t 10 years
• Ending Value 100 x (1.10) 10 259.37

9

• Annualized Rate of Return
• Converting Returns for time periods other than
  one year into annualized returns
• Rear (1
  HPR)
• where Rear effective annual interest rate
• HPR holding period
  rate of return
• adjustment
  factor determined by whether
• holding
  period is measured in days, weeks,
• months,
  quarters, etc.

10
Expected Return

• Probability Distribution
• E(return)P1xR1 P2xR2 PnxRn

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A Portfolios Expected Rate of Return

• Same formula as HPR for security, or
• Weighted average rate of return W1 x E(R1)
• W2 x E(R2) . . . Wn x E(Rn)
• where Wi of portfolio invested in
  security i,
• E(Ri) the per-period return on
  security i, and
• W1 Wn 1

12
Geometric Mean Return

• Value of compounded per-period average rate of
  return of financial asset determined during
  specified time
• HPRR PPRR1 x PPRR2 x x PPRRn
• GMR HPRR(1 ? n) 1

13
Arithmetic Mean Return

• Simple average return found by dividing sum of
  separate per-period returns by number of periods
  over which they were earned

14
Why Arithmetic Mean Is a Really Bad Measure of
Returns Over Time

• R1 100 R2 50
• Arithmetic average return 25
• Geometric mean return 0

15
Relationship between GM and Arithmetic Mean
Returns

• Only when all PPRs are identical will GMR and
  arithmetic mean be equal
• If PPRs are not identical, then GMR will always
  be less than arithmetic mean return
• Difference increases as variability among PPRs
  increases

16
Predicting Future Performance Based on Past
Performance

• If predicting one period in future, use
  arithmetic mean
• If predicting n periods in future, where n
  number of historical periods, use GMR

17
Risk

• Pure Risk versus Speculative Risk
• Types of Risk
• Purchasing power (or inflation) risk
• Interest rate risk
• Market risk
• Business (and default) risk
• Liquidity risk
• Political (sovereign) risk
• Exchange rate risk
• Tax risk
• Additional commitment Risk

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• Pure Risk
• Involves only chance of loss but no chance of
  gain
• Speculative Risk
• Associated with speculation in which there is
  some chance of gain and some chance of loss

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Purchasing Power Risk

• Loss of purchasing power of investment assets
  future cash flows
• 1 real rate (1 nominal rate) ? (1
  inflation rate)real rate nominal rate
  inflation rate

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• Interest Rate Risk
• for debt securities, risk associated with changes
  in interest rates consists of price risk and
  reinvestment rate risk
• Price Risk
• a change in market interest rates produces an
  opposite change in the value of investments
• Reinvestment Rate Risk
• risk as to what interest rate will be when income
  and/or principal from investments are reinvested

21
Market Risk

• Degree to which assets return is affected by
  events affecting entire market
• Also called systematic risk
• Risk that is nondiversifiable

22
Business Risk

• Unique for each enterprise
• Also called nonsystematic risk
• Risk that can be reduced or eliminated through
  diversification

23
Default Risk

• Risk that contractual payments will not be honored

24
Financial Risk

• Risk that companies with heavy use of debt
  financing will have more volatile rates of return

25
Liquidity Risk

• Relative inability to convert an asset to cash
  quickly, at any time, and without any loss of
  principal

26
Political (Sovereign) Risk

• Degree to which investment asset subject to
  events in foreign markets that can cause the
  value of these investments to drop precipitously
• Includes
• effects of trade disputes
• wars
• political unrest
• tariffs
• corruption
• expropriation

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Exchange Rate Risk

• Degree to which investment asset affected by
  movements in currency exchange rates in country
  where investment is located
• Affects investments in some U.S. companies
  because of overseas markets, production
  facilities, and raw materials

28
Tax Risk

• Extent to which investments returns are exposed
  to changes in tax laws
• Income that is not currently taxable may be
  taxable later

29
Investment Manager Risk

• Risk that managed fund will perform below average
  due to poor investment decisions
• Can minimize risk through diversification or use
  of index funds

30
Additional Commitment Risk

• Degree to which investment asset may require the
  buyer to put additional money into that
  investment
• Inability to meet commitment might create loss of
  value

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Measures of Risk

• Range
• Semivariance

• Standard Deviation
• Coefficient of Variation
• Beta

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Why Is Risk Important?

• It is the driver for expected return

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Standard Deviation

• Measure of degree of dispersion of distribution
• - Standard deviation is square root of the
  variance
• Normal distribution
• - Two times out of three actual value will be
  within one standard deviation on either side of
  mean value
• - 19 out of 20 times will be within two standard
  deviations
• - Well diversified portfolios with a large
  number of stocks have rates of return that
  approximate a normal distribution

34
Computing Variance and Standard Deviation
Using Historical (ex post) data
35
Skewness

• Distribution of returns have one tail which is
  
• longer than the other
• Investors prefer returns that are skewed to
  the right

Kurtosis

• Measures the peakedness of a distribution
• - leptokurtic refers to a distribution that
  has a
• very high center with thick tails
• - platykurtic is a distribution with short
  center
• and negligible tails

36
Monte Carlo Simulation

• Technique using repeated samplings from a
• probability distribution to determine the
• distribution of the dollar value of a
  portfolio
• - Assumes returns are generated by a random
  distribution
• process
• - Results are dependent upon the mean and
  standard
• distribution of the hypothesized
  distribution
• - Useful tool to simulate both the
  accumulation and
• decumulation of a portfolio

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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

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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
• 30 on short positions
• In-house, only higher, never lower

39
Buying Power

• Dollar value of additional securities that can be
  purchased on margin with current equity in margin
  account

40
Net Equity

• Total value of account minus amount of debt
  outstanding (with respect to a margin account)
• E MV LOAN 
• where MV market value of portfolio
• LOAN current loan balance

41
Maintenance Margin

• Minimum percentage of equity that ongoing margin
  account is required to maintain at all times
• MV x (1 MMR) LOAN
• where MMR maintenance margin rate

42
Ways to Satisfy Margin Call

• Deposit cash in account
• Add more collateral (marginable securities) to
  account.
• Sell stock from account and use proceeds to
  reduce the margin debt
• In each case, result must raise equity
  percentage to margin maintenance minimum to
  satisfy margin call.

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Cash Necessary to Meet a Margin Call

• Cash added LOAN MV x (1 MMR)
• Example
• Loan 50,000
• MV 60,000
• MMR 30
• Cash added 50,000 60,000 x (1 - .30)
• 8,000

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Permitted Cash Withdrawals

• Maximum Cash Withdrawal
• MV x (1 IMR) LOAN
• Example
• MV 100,000,
• IMR 60,
• LOAN 15,000
• Max. Cash W/D 100,000 x (1 .60)15,000
• 25,000

45
The Impact of Leverage

• ROA (Ending Value Beginning Value) ?
  Beginning Value
• ROE (Ending Value Beginning Value)
  Interest Charges ? Initial Investment

46
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