Engineering Management 452 Advanced Financial Management

1
Engineering Management 452 Advanced Financial
Management

• Chapter 6
• The Financial Environment Risk and Rates of
  Return

2
Introduction

• Investors like returns and dislike risks
• All financial assets are expected to produce cash
  flows, and the risk of an asset is judged in
  terms of its cash flows

3
Risk and Return

• Risk chance of unfavorable event
• Measured by distribution and standard deviations.
• Expected returns weighted average of returns.
• Investors have different tolerance for risk
  (averse)

4
Risk and Return

• All financial assets are expected to produce cash
  flows, and the riskiness of an asset is judged in
  terms of the riskiness of its cash flow.
• The riskiness of an asset can be considered in
  two ways (1) on a stand-alone basis or (2) in a
  portfolio context.
• In a portfolio context, an assets risk can be
  divided into two components (1) diversifiable
  risk component, which can be eliminated, and (2)
  a market risk component, which cannot be
  eliminated.
• Only market risk is relevant. Diversifiable risk
  is irrelevant because it can be eliminated.

5
Risk and Return

• Only knowing the expected return of two assets is
  insufficient to determine whether one is
  preferable to another. We also need to know the
  variability of the returns (variance or standard
  deviation).
• The expected return is equal to the product of
  the probability of the outcome occurring and the
  rate of return if the outcome occurs.
• The tighter the probability distribution, the
  smaller the risk. The variance or standard
  deviation of returns measures the tightness of
  the probability distribution.
• The coefficient of variation measures the risk
  return trade-off or the risk per unit of return.
  It is defined as the standard deviation divided
  by the expected return.
• In a market dominated by risk-averse investors,
  riskier securities must have higher expected
  returns.

6
Probability Distribution
Firm X
Firm Y
Rate of return ()
100
15
0
-70
Expected Rate of Return
7
Historical Performance of various Investments

• Historical returns

8
Portfolio analysis

• Expected return of portfolio is the weighted
  average of individual returns.
• Standard deviation of the portfolio is different
  based on correlation coefficient.

9
Risk in a portfolio context

• An asset held as part of a portfolio is less
  risky than the same asset held alone. From an
  investors standpoint, the fact that a particular
  stock goes up or down is not very important, what
  is important is the return on his or her
  portfolio, and the portfolios risk.
• The expected return on a portfolio is the
  weighted average of the expected returns on the
  individual assets in the portfolio.
• On average, most stocks are positively
  correlated, but not perfectly so. Combining
  stock that are not perfectly positively
  correlated reduces risk but does not eliminate it
  completely.
• Almost half of the riskiness inherent in an
  average individual stock can be eliminated if the
  stock is held in a reasonably well-diversified
  portfolio (40 stocks).

10
Impact of portfolio size
?p ()
35 18 0
Diversifiable Risk
Market Risk
10 20 30 40 2000
Stocks in Portfolio
11
Capital Asset Pricing Model CAPM

• Stock risk is measured by volatility (beta).
• The Security Market Line (SML) determines
  required rate of return based on the firms beta.

12
What is the CAPM?

• The CAPM is an equilibrium model that specifies
  the relationship between risk and required rate
  of return for assets held in well-diversified
  portfolios.
• It is based on the premise that only one factor
  affects risk.

13
What are the assumptions of the CAPM?

• Investors all think in terms ofa single holding
  period.
• All investors have identical expectations.
• Investors can borrow or lend unlimited amounts at
  the risk-free rate.

14
Security and Portfolio Beta

• Beta measures a stocks volatility relative to an
  average stock (beta 1.0).
• Beta for an individual stock is calculated and
  published by numerous investment services.
• Most stocks have betas in the range of 0.5 to
  1.5, whereas the average is 1.0 by definition.
• Since a stocks beta measures its contribution to
  the riskiness of a portfolio, beta is the
  theoretically correct measure of the stocks
  riskiness.
• The beta of a portfolio of stocks is the weighted
  average of the betas of the individual stocks
  within the portfolio.

15
How are betas calculated?

• Run a regression line of past returns on Stock i
  versus returns on the market.
• The regression line is called the characteristic
  line.
• The slope coefficient of the characteristic line
  is defined as the beta coefficient.

16
Illustration of beta calculation
.
20 15 10 5
.
Year kM ki 1 15 18 2 -5 -10
3 12 16
_
-5 0 5 10 15 20
kM
-5 -10


.
ki -2.59 1.44 kM
17
How do you find beta?

• Computer In the real world, analysts use a
  computer with statistical or spreadsheet software
  to perform the regression.
• At least a years worth of weekly or monthly
  returns are used.
• Most analysts use 5 years of monthly returns.

(More...)
18
How do you find beta?

• By Eye Plot points, draw in regression line
  slope is rise/run.The rise is the difference in
  ki,the run is the difference in kM.
• Calculator Enter the data points and use the
  least squares regression function
• ki a bkM -2.59 1.44 kM.

(More...)
19
Beta Significance

• If beta 1.0, stock is average risk.
• If beta gt 1.0, stock is riskier than average.
• If beta lt 1.0, stock is less risky than average.
• Most stocks have betas in the range of 0.5 to 1.5.

20
Betas
21
Security Market Line

• The market risk premium is the additional return
  over the risk free rate needed to compensate
  investors for assuming an average amount of risk.
• You can measure a stocks relative riskiness by
  its beta coefficient.
• The required return for any investment is equal
  to the risk-free return plus a premium for risk.
• Required return for stock i (risk-free rate)
  (market risk premium)(stock is beta).
• Where the market risk premium is equal to the
  required return on the market minus the risk-free
  rate.

22
What does the SML tell us?

• The expected rate of return on any efficient
  portfolio is equal to the risk-free rate plus a
  risk premium.
• The optimal portfolio for any investor is the
  point of tangency between the SML and the
  investors indifference curves.

23
Security Market Line (SML)
Required Rate of Return k ()
18 15 11 8
Hibeta
kM
SML
kRF
Lobeta
0 0.5 1.0 1.5 2.0
24
Impact of inflation and increased risk aversion
Required Rate of Return k ()
RISK
SML3
INFLATION
SML2
SML1
18 15 11 8
Original situation
0 0.5 1.0 1.5 2.0