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

1. Only when all PPRs are identical will GMR and
   arithmetic mean be equal
2. If PPRs are not identical, then GMR will always
   be less than arithmetic mean return
3. 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

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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

31
Measures of Risk

• Range
• Semivariance

• Standard Deviation
• Coefficient of Variation
• Beta

32
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

37
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

38
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