Slides_Fundamentals of Investments - Chapter 19 potx

Performance Evaluation & Risk ManagementOur goal in this chapter is to examine the methods of c evaluating risk- adjusted investment performance, and d assessing and managing the risks i

C h a p t e r

Performance Evaluation and

R isk Management

Performance Evaluation and

R isk Management

second edition

Fundamentals

of Investments

Valuation & Management

Charles J Corrado Bradford D.Jordan

McGraw Hill / Irwin Slides by Yee-Tien (Ted) Fu

that I am concerned about.

It is the return of my investment!”

– Will Rogers

Performance Evaluation & Risk Management

Our goal in this chapter is to examine the methods of c evaluating risk-

adjusted investment performance, and d assessing and managing the risks involved with specific

investment strategies

Goal

Can anyone consistently earn an “excess”

return, thereby “beating” the market?

Performance evaluation

Concerns the assessment of how well a money manager achieves a balance between high returns and acceptable risks

Performance Evaluation Measures

Š The raw return on a portfolio, R P, is the total

% return on the portfolio with no adjustment for risk or comparison to any benchmark

Š It is a naive measure of performance

evaluation that does not reflect any consideration of risk As such, its usefulness is limited

Š The Sharpe ratio is a reward-to-risk ratio that

focuses on total risk

Š It is computed as a portfolio’s risk premium

divided by the standard deviation for the portfolio’s return

f

p R

R −

=

Work the Web

 Visit Professor Sharpe at:

http://www.stanford.edu/~wfsharpe

Š The Treynor ratio is a reward-to-risk ratio that

looks at systematic risk only

Š It is computed as a portfolio’s risk premium

divided by the portfolio’s beta coefficient

Performance Evaluation Measures

Jensen’s Alpha

Š Jensen’s alpha is the excess return above or

below the security market line It can be interpreted as a measure of how much the portfolio “beat the market.”

Š It is computed as the raw portfolio return less

the expected portfolio return as predicted by the CAPM

Comparing Performance Measures

Sharpe ratio

Š Appropriate for the evaluation of an entire

portfolio

Š Penalizes a portfolio for being undiversified,

substantially different, which performance measure should we use?

Comparing Performance Measures

Treynor ratio / Jensen’s alpha

Š Appropriate for the evaluation of securities or portfolios for possible inclusion in a broader or

“master” portfolio

Š Both are similar, the only difference being that the Treynor ratio standardizes everything,

including any excess return, relative to beta

Š Both require a beta estimate (and betas from

different sources may differ a lot)

 The performance measures we have

discussed are commonly used in the evaluation of mutual funds See, for

example, the Ratings and Risk for

various funds at:

http://www.morningstar.com

Sharpe-Optimal Portfolios

Š A funds allocation with the highest possible

Sharpe ratio is said to be Sharpe-optimal.

Š To find the Sharpe-optimal portfolio, consider the plot of the investment opportunity set of risk-return possibilities for a portfolio

Expected Return

Expected Return

Sharpe-Optimal Portfolios

of the efficient portfolios on the Markowitz efficient frontier.

Investment Risk Management

Š We will focus on what is known as the at-Risk approach

Value-Investment risk management

Concerns a money manager’s control over investment risks, usually with respect to potential short-run losses

Š If the returns on an investment follow a normal distribution, we can state the probability that a portfolio’s return will be within a certain range given the mean and standard deviation of the

Assesses risk by stating the probability of a loss a portfolio may experience within a

fixed time horizon

Value-at-Risk (VaR)

Example: VaR

Š Suppose you own an S&P 500 index fund

Historically, E(R S&P500 ) ≈ 13% per year, while σS&P500

≈ 20% What is the probability of a return of -7% or worse in a particular year?

— The odds of being within one σ are about 2/3 or 67 I.e Prob (.13–.20 ≤ RS&P500 ≤ 13+.20) ≈ 67

or Prob (–.07 ≤ R S&P500 ≤ 33) ≈ 67

— So, Prob (R S&P500 ≤ –.07) ≈ 1/6 or 17

— The VaR statistic is thus a return of –.07 or worse

with a probability of 17%.

 Learn all about VaR at:

http://www.gloriamundi.org

More on Computing Value-at-Risk

Example: More on VaR

Š For the S&P 500 index fund, what is the probability

of a loss of 30% or more over the next two years?

— 2-year average return = 2×.13 = 26

— 1-year σ 2 = 20 2 = 04 So, 2-year σ 2 = 2×.04 = 08.

So, 1-year σ = √.08 ≈ 28

— The odds of being within two σ ’s are 95.

I.e Prob (.26–2×.28 ≤ R S&P500 ≤ 26+2×.28) ≈ 95

or Prob (–.30 ≤ R S&P500 ≤ 82) ≈ 95

— So, Prob (R S&P500 ≤ –.30) ≈ 2.5%

( ) ( )R E R T

E p,T = p ×

T

p T

326

2Prob

R E R

T T

R E R

p p

T p

p p

T p

Work the Web

 Learn about the risk management

profession at:

http://www.garp.org

Î Performance Evaluation Measures

• The Sharpe Ratio

• The Treynor Ratio

• Jensen’s Alpha

Š Comparing Performance Measures

Î Sharpe-Optimal Portfolios