Investing Choices and Risk Measures

1
Investing Choices and Risk Measures
Chapter 8
11/14/2009 422 AM

• In this part, (starting from the previous
  chapter), we maintain the same assumptions.
• We assume perfect markets, so we assume four
  market features
• 1. No differences in opinion.
• 2. No taxes.
• 3. No transaction costs.
• 4. No big sellers/buyerswe have infinitely
  many clones that can buy or sell.
• We already allow for unequal rates of returns in
  each period.
• We already allow for uncertainty. So, we do not
  know in advance what the rates of return on every
  project are.
• But in contrast to Chapters 6, we no longer
  assume risk-neutrality. We are allowing for risk
  aversion now.
• Recall Chapter 4, in which we found out that you
  are risk-averse.
• In this chapter, we lay the groundwork for
  understanding how investors choose among many
  different projects.
• You need this a to think as a manager about
  your companys investment risk b more
  importantly to think about your opportunity cost
  of capital, ?(r).

References A First Course Corporate Finance
(Welch, 2009).
2
Some Particular Investments, in PERCENT
8-1

• (These numbers are intentionally different from
  those in the book.)
• B may not be better than A if you care about Blue
  (you may be unemployed in Blue)unless you assume
  that you care about certain characteristics only,
  such as risk and reward, and consider all states
  similarly. We will assume this henceforth.
• Consider E (4.0,4.0,4.0,4.0). Would a
  risk-neutral/risk-averse investor prefer B to E
  (as sole investment)?
• Consider E(3.9,3.9,3.9,3.9). Would a
  risk-neutral/risk-averse investor prefer B to E
  (as sole investment)?
• Consider E(4.1,4.1,4.1,4.1). Would a
  risk-neutral/risk-averse investor prefer B to E
  (as sole investment)?

3
Measuring Risk and Reward
8-1B, 1C

• Portfolio Reward
• Portfolio Risk
• Reminder If these returns were not the
  population, but just representative historical
  realizations from a population, you would divide
  by 3, not by 4 in your computation of the
  variance.

4
(The second has a line over it. Tough to see.
Powerpoint---yucc)
Overbar-ed
Overbar-ed
Overbar-ed
Overbar-ed
5
Risk of Portfolio vs. Components

• Important The standard deviation as a measure of
  risk applies only to your overall portfolio, not
  to individual securities within your portfolio.

6
Diversification
8-2

• .

7
Effects of Co-Movement
8-3
8
Own Risk
8-3A, 3B
9
Effects of Co-Movement
8-3
10
8-3A, 3B

• Important
• The fundamental insight of investments Investors
  care about overall portfolio risk, not about the
  constituent component risk.
• From a corporate managerial perspective, it is
  not your projects that are low risk in themselves
  that are highly desirable for your investors, but
  projects which wiggle opposite to the rest of
  their portfolios

11
Covariance, Beta, Correlation
8-3C

• We need a numerical measure of synchronicity of
  securities with portfolios.

12
Overbar-ed
Overbar-ed
Overbar-ed
Cov(A,C) Cov(A,D)
13
Which One?
8-3C

• Consider A our base (market) portfolio.
• Covariance has units that cannot be interpreted.
  Yuck.
• Correlation has a magnitude problem.
• Consider two portfolio additions, different
  mutual funds
• D1 (0.3,1.3,0.3,-0.7) and D2(30,130,30,-70).
• Adding 10 of D1 to your A portfolio would
  increase your risk less than adding 10 of D2.
• The correlation ignores this scale difference.
  It is -70.7 in either case.
• Beta does not ignore this. It is -0.1 for D1 and
  10 for D2.
• Therefore, we prefer measuring risk contribution
  of B or C by its market beta with respect to A.

14
Plots
15
Beta
8-3C

• Beta is similar to correlation. It always has the
  same sign.
• Beta can be interpreted as a slope. Put A (M) on
  the X axis, and your project B (or C) on the Y
  axis. A slope of 1 is a diagonal line. A slope
  of 0 is a horizontal line. A slope of 8 is a
  vertical line.
• Beta tells you how an x higher rate of return
  (than normal) in the market portfolio will likely
  reflect itself simultaneously in a ßi x
  higher rate of return in your stock.
• If you also have alpha, then beta can be
  interpreted as giving you the best conditional
  forecast of your projects rate of return, given
  a market outcome scenarios rate of return. You
  do not need the (than normal) qualification.
• (I put the y-axis as the first subscript on beta,
  and the x-axis second. If I omit the second
  subscript, I mean the overall market portfolio.)
• Estimating market-beta from historical data is
  discussed in 8-3D. (Also, perhaps look at some
  sample betas in Yahoo!Finance.)

16
Preferences and Equilibrium Preview
8-3
17
Market-Beta Weighted Averaging
8-4
18
Overbar-ed
Overbar-ed
19
Time and Risk

• Var( RP ) wA2Var(RA) wB2Var(RB)
  2wAwBcov(RA,RB)(Note You can check the
  above formula with previous examples.)
• Returns are roughly uncorrelated over time.
• Returns are roughly additive (except for
  compounding).
• Assume per-year variance is constant. Call it V.
  (Market (20)2).
• R2Years RYear1 RYear2
• Var(R2Years)
• Variance grows with T. SD grows with .
• Sharpe Ratio (Mean/SD) changes

20
Homework Assignment

• 1. Reread Chapter 8.
• 2. Read Chapter 9.
• 3. Hand in all Chapter 8 end-of-chapter problems,
  due in 7 days.