Risk and Rates of Return

1
Chapter 6

• Risk and Rates of Return

2
Chapter 6 Objectives

• Inflation and rates of return
• How to measure risk
• (variance, standard deviation, beta)
• How to reduce risk
• (diversification)
• How to price risk
• (security market line, CAPM)

3
Historical Risk and Return

• Annual From 1926 to 1999
• Avg. Return Std Dev.
• Small Stocks 17.6 33.6
• Large Co. Stocks 13.3 20.1
• L-T Corp Bonds 5.9 8.7
• L-T Govt. Bonds 5.5 9.3
• T-Bills 3.8 3.2
• Inflation 3.2 4.6

4
Why are these rates different?

• 90-day Treasury Bill 1.7
• 90-day Commercial Paper 1.8
• 2-year US Treasury Note 3.0
• 10-year US Treasury Note 5.0
• 10-year Corporate Bond 6.9

5
Inflation, Rates of Return, and the Fisher Effect
6
Interest Rates
Conceptually
7
Interest Rates
8
Interest Rates
9
Interest Rates
10
Interest Rates
11
Interest Rates

• Suppose the real rate is 3, and the nominal rate
  is 8. What is the inflation rate premium?
• (1 krf) (1 k) (1 IRP)
• (1.08) (1.03) (1 IRP)
• (1 IRP) (1.0485), so
• IRP 4.85

12
Term Structure of Interest Rates

• The pattern of rates of return for debt
  securities that differ only in the length of time
  to maturity.

13
Term Structure of Interest Rates

• The pattern of rates of return for debt
  securities that differ only in the length of time
  to maturity.

14
Term Structure of Interest Rates

• The pattern of rates of return for debt
  securities that differ only in the length of time
  to maturity.

15
Term Structure of Interest Rates

• The yield curve may be downward sloping or
  inverted if rates are expected to fall.

16
Term Structure of Interest Rates

• The yield curve may be downward sloping or
  inverted if rates are expected to fall.

17
Recent US Treasury Yield Curve
18
For a Treasury security, what is the required
rate of return?

• Since Treasuries are essentially free of default
  risk, the rate of return on a Treasury security
  is considered the risk-free rate of return.

19
For a corporate stock or bond, what is the
required rate of return?
20
For a corporate stock or bond, what is the
required rate of return?
21
For a corporate stock or bond, what is the
required rate of return?

• How large of a risk premium should we require to
  buy a corporate security?

22
Returns

• Expected Return - the return that an investor
  expects to earn on an asset, given its price,
  growth potential, etc.
• Required Return - the return that an investor
  requires on an asset given its risk and market
  interest rates.

23
Holding Period (Actual) Returns

• The realized return over a period of time (HPR).
• HPR(Ending Price - Beginning Price
  Distributions Received)/Beginning Price
• Example What is your HPR if you buy a stock for
  20, receive 1 in dividends, and then sell it
  for 25.
• HPR (25-201)/20 0.3 30

24
Calculation of Expected Returns

• Expected Rate of Return (Expected Value) given a
  probability distribution of possible returns(ki)
  E(k) or k
• _ n
• E(k)k ?? ki P(ki)
• i1
• Realized or Average Return on Historical Data
• - n
• k 1/n ??k i
• i1

25
Expected Return and Standard Deviation Example

• MAD E(r) .25(80) .60(30) .15(-30)
  33.5
• CON E(r) .25(5) .60(10) .15(15) 9.5

26
Definition of Risk

• Risk is an uncertain outcome or chance of an
  adverse outcome.
• Concerned with the riskiness of cash flows from
  financial assets.
• Namely, the chance that actual cash flows will be
  different from forecasted cash flows.
• Standard Deviation can measure this type of risk.

27
How do we Measure Risk?

• A more scientific approach is to examine the
  stocks standard deviation of returns.
• Standard deviation is a measure of the dispersion
  of possible outcomes.
• The greater the standard deviation, the greater
  the uncertainty, and therefore , the greater the
  risk.

28
Standard Deviation

• (ki - k)2 P(ki)

29
Expected Return and Standard Deviation Example

• MAD E(r) .25(80) .60(30) .15(-30)
  33.5
• CON E(r) .25(5) .60(10) .15(15) 9.5

30

• MAD, Inc.
• ( 80 - 33.5)2 (.25) 540.56
• (30 - 33.5)2 (.6) 7.35
• (-30 - 33.5)2 (.15) 604.84 Variance
  1152.75
• Stand. dev. 1152.75 34.0

31
Expected Return and Standard Deviation Example

• MAD E(r) .25(80) .60(30) .15(-30)
  33.5
• CON E(r) .25(5) .60(10) .15(15) 9.5

32

• Contrary Co.
• (5 - 9.5)2 (.25) 5.06
• (10 - 9.5)2 (.6) 0.15
• (15 - 9.5)2 (.15) 4.54
• Variance 9.75
• Stand. dev. 9.75 3.1

33

• Which stock would you prefer?
• How would you decide?

34

• Which stock would you prefer?
• How would you decide?

35

• It depends on your tolerance for risk!
• Remember, theres a tradeoff between risk and
  return.

36
Coefficient of Variation

• A relative measure of risk. Whereas, s is an
  absolute measure of risk.
• Relates risk to expected return.
• CV s/E(k)
• MADs CV 34/33.5 1.01
• CONs CV 3.1/9.5 0.33
• CONtrary is the less risky of the two
  investments. Would choose CON if risk averse.

37
Portfolios

• Expected Portfolio Return is weighted average of
  the expected returns of the individual stocks
  Swjkj.
• However, portfolio risk (standard deviation) is
  NOT the weighted average of the standard
  deviations of the individual stocks.
• Combining several securities in a portfolio can
  actually reduce overall risk.
• How does this work?

38
Suppose we have stock A and stock B. The returns
on these stocks do not tend to move together over
time (they are not perfectly correlated).
39
What has happened to the variability of returns
for the portfolio?
40
Diversification

• Investing in more than one security to reduce
  risk.
• If two stocks are perfectly positively
  correlated, diversification has no effect on
  risk.
• If two stocks are perfectly negatively
  correlated, the portfolio is perfectly
  diversified.

41

• If you owned a share of every stock traded on the
  NYSE and NASDAQ, would you be diversified?
• YES!
• Would you have eliminated all of your risk?
• NO! Common stock portfolios still have risk.

42
Some risk can be diversified away and some cannot.

• Market risk (systematic risk) is
  nondiversifiable. This type of risk cannot be
  diversified away.
• Company-unique risk (unsystematic risk) is
  diversifiable. This type of risk can be reduced
  through diversification.

43
Market Risk

• Unexpected changes in interest rates.
• Unexpected changes in cash flows due to tax rate
  changes, foreign competition, and the overall
  business cycle.

44
Company-unique Risk

• A companys labor force goes on strike.
• A companys top management dies in a plane crash.
• A huge oil tank bursts and floods a companys
  production area.

45

• As you add stocks to your portfolio,
  company-unique risk is reduced.

46

• As you add stocks to your portfolio,
  company-unique risk is reduced.

47
Do some firms have more market risk than others?

• Yes. For example
• Interest rate changes affect all firms, but which
  would be more affected
• a) Retail food chain
• b) Commercial bank

48
Note

• The market compensates investors for accepting
  risk - but only for market risk. Company-unique
  risk can and should be diversified away.
• So - we need to be able to measure market risk.

49
This is why we have Beta.

• Beta a measure of market risk.
• Specifically, beta is a measure of how an
  individual stocks returns vary with market
  returns.
• Its a measure of the sensitivity of an
  individual stocks returns to changes in the
  market.

50
The Concept of Beta

• Beta(b) measures how the return of an individual
  asset (or even a portfolio) varies with the
  market portfolio.
• b 1.0 same risk as the market
• b lt 1.0 less risky than the market
• b gt 1.0 more risky than the market
• Beta is the slope of the regression line (y a
  bx) between a stocks return(y) and the market
  return(x) over time, b from simple linear
  regression.
• bi Covariancei,m/Mkt. Var. rimsism/sm2

51
Relating Market Risk and Required Return the CAPM

• Heres the word story a stocks required rate of
  return risk-free rate the stocks risk
  premium.
• The main assumption is investors hold well
  diversified portfolios only concerned with
  market risk.
• A stocks risk premium measure of systematic
  risk X market risk premium.

52
CAPM Equation

• krp market risk premium km - krf
• stock risk premium bj(krp)
• kj krf bj(km - krf )
• krf bj (krp)
• Example What is Yahoos required return if its b
  1.75, the current 3-mo. T-bill rate is 1.7,
  and the historical market risk premium of 9.5 is
  demanded?
• Yahoo k 1.7 1.75(9.5) 18.3

53
Question If Yahoos exp. Return 15, what to
do?
54
Portfolio Beta and CAPM

• The b for a portfolio of stocks is the weighted
  average of the individual stock bs.
• bp Swjbj
• Example The risk-free rate is 6, the market
  return is 16. What is the required return for a
  portfolio consisting of 40 AOL with b 1.7, 30
  Exxon with b 0.85, and 30 Fox Corp. with b
  1.15.
• Bp .4(1.7).3(0.85).3(1.15) 1.28
• kp 6 1.28(16 - 6) 18.8

55
More SML Fun!

• According to the CAPM and SML equation with k
  6 b(16 - 6)
• How would a change in inflation affect required
  returns? (Say inflation increases 2 points)
• How would a change in risk aversion (market risk
  premium) affect required returns? (Say market
  risk premium decreases 2 points.)

56
Changes to SML
57
Changes to SML
58
Changes to SML
59
Limitations of CAPM/SML

• Dont really know what the market portfolio is,
  which makes it hard to estimate market expected
  or required return.
• Beta estimates can be unstable and might not
  reflect the future.
• Maturity debate over proper risk-free estimate.
• Most investors focus on more than systematic
  risk.