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## Risk and Return

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### Financial Crisis

- Define risk, risk aversion, and risk-return tradeoff.
- Measure risk.
- Identify different types of risk.
- Explain methods of risk reduction.
- Describe how firms compensate for risk.
- Discuss the CAPM.

The failure of one company can lead to the failure of others

If AIG had been allowed to fail it likely would have taken many other companies with it

Financial Crisis

- This risk is sometimes referred to as “systematic risk”, or Market Risk
- Systematic risk cannot be diversified away (because it affects everyone)
- Sometimes different groups of assets go up and down together in value, (i.e., all software companies)

Risk and Rates of Return

- Risk is the potential for unexpected events to occur or a desired outcome not to occur.
- If two financial alternatives are similar except for their degree of risk, most people will choose the less risky alternative because they are risk averse, i.e. they don’t like risk.

Risk and Rates of Return

- Risk averse investors will require higher expected rates of return as compensation for taking on higher levels of risk than someone who is risk tolerant (more willing to take on risk.) Axiom 1

Measuring Risk

- We can never avoid risk entirely, i.e., getting out of bed or staying
- Measuring risk is difficult; it depends on the degree of uncertainty in a situation
- The greater the probability of an uncertain outcome, the greater the degree of risk (i.e., drilling for oil)

Expected Return & Standard Deviation

- Most decisions have a number of different possible outcomes or returns
- Expected return is the mean, the average of a set of values, of the probability distribution of possible outcomes. i.e., sales projections
- Future returns are not known with certainty. The standard deviation is a measure of this uncertainty.

Expected Return

- To calculate expected return, compute the weighted average of possible returns

where

m= Expected return

Vi = Possible value of return during period i

Pi = Probability of V occurring during period i

m = S(Vi x Pi)

State of Economy Probability Return

Economic Downturn .10 –5%

Zero Growth .20 5%

Moderate Growth .40 10%

High Growth .30 20%

Expected Return CalculationExample:

You are evaluating Zumwalt Corporation’s common stock. You estimate the following returns given different states of the economy

= – 0.5%

= 1.0%

= 4.0%

= 6.0%

k = 10.5%

Expected rate of return on the stock is 10.5%

Zumwalt Corp

Probability

of Return

Probability

of Return

100%

40%

30%

20%

10%

Return

Return

–5%

5%

10%

20%

6%

Measurement of Investment RiskExample:

You evaluate two investments: Zumwalt Corporation’s common stock and a one year Gov't Bond paying a guaranteed 6%.

There is risk in owning Zumwalt stock, no risk in owning the T-bills

Link to Society for Risk Analysis

Standard Deviation

- A numerical indicator of how widely dispersed the possible values are around a mean (Fig. 7-1) p. 164
- The more widely dispersed (Bold), the larger the standard deviation, and the greater the risk of unexpected values
- The closer dispersed (Calm), the lower the standard deviation, and the lesser the risk of unexpected values.

s2 = .005725 = 0.5725%

- = SQRT of 0.005725
- = .07566 = 7.566%

s = SQRT(SP(V - m)2)

State of Economy Probability Return

Economic Downturn .10 5%

Zero Growth .20 5%

Moderate Growth .40 10%

High Growth .30 20%

Measurement of Investment Risk- Standard Deviation (s) measures the dispersion of returns. It is the square root of the variance.

Example:

Compute the standard deviation on Zumwalt common stock. the mean (m) was previously computed as 10.5%

(- - 10.5%)2 = .24025%

( - 10.5%)2 = .0605%

( - 10.5%)2 = .001%

( - 10.5%)2 = .27075%

Measurement of Investment Risk

- The standard deviation of 7.566% means that Zumwalt’s return would be in the 10.5% range (the mean), plus or minus 7.566%!
- That ‘s a very wide range! High Risk!
- 10.5 + 7.566 = 18.066
- 10.5 – 7.566 = 2.934
- And this holds true for one standard deviation, or only 2/3 of the time
- The other 1/3 of the time it could be above or below the standard deviation!

Measuring Risk

- Review standard deviations, Calm vs Bold on page 166
- See Fig 7-3, page 168 for comparison of Calm vs Bold for one and two standard deviations
- Calculate coefficient of variation, page

168, (Standard Deviation / Mean)

Calm 15.5% (low risk <20%) vs Bold 38.5% (high risk >30%). Zumwalt 7.566/10.5 = 72.1%!

Risk and Rates of Return

Risk of a company's stock can be separated into two parts:

- Firm Specific Risk - Risk due to factors within the firm

- Market related Risk - Risk due to overall market conditions

Stock price will most likely fall if a major government contract is discontinued unexpectedly.

Stock price is likely to rise if overall stock

market is doing well.

- Diversification: If investors hold stock in many companies, the firm specific risk will be cancelled out.

Even if investors hold many stocks, cannot eliminate the market related risk

Diversifiable vs Non-diversifiable

- Diversifiable risk (company specific) affects only one company, - give examples
- Non-diversifiable risk (market risk), affects all companies, - give examples – credit/liquidity crisis
- How many stocks in the DJIA?
- Discuss recent changes in the DOW
- See fig 7-4, page 174; demonstrates how diversification cancels out risk

# of stocks in Portfolio

Risk and Rates of Return- Risk and Diversification
- Total investment risk is composed of two types, firm specific risk (top) and market related risk (bottom). Both affect stock price.

Total Risk

# of stocks in Portfolio

Risk and Rates of Return- Risk and Diversification
- If an investor holds enough stocks in portfolio (about 20) company specific (diversifiable) risk is virtually eliminated

Market Related Risk

# of stocks in Portfolio

Risk and Rates of Return- Risk and Diversification
- When company specific risk is eliminated, then all you have left is market related (non diversifiable) risk that applies to all investments

Firm Specific Risk

Measuring & Understanding Market Risk

- Market risk is the risk of the overall market, so to measure we need to compare individual stock returns to the overall market returns.
- A proxy for the market is usually used: An index of stocks such as the S&P 500
- Market risk measures how individual stock returns are affected by total market returns
- So let’s compare the returns of PepsiCo to the S & P 500

Return

15%

10%

5%

S&P

Return

-15%

-10%

-5%

5%

10%

15%

-5%

-10%

-15%

Risk and Rates of Return- Regress individual stock returns on Market index

Jan 1999

PepsiCo -0.37%

S&P -1.99%

Return

15%

10%

5%

S&P

Return

-15%

-10%

-5%

5%

10%

15%

-5%

-10%

-15%

Risk and Rates of Return- Regress individual stock returns on Market index

Plot Remaining Points

Return

15%

10%

5%

S&P

Return

-15%

-10%

-5%

5%

10%

15%

-5%

-10%

-15%

Risk and Rates of ReturnRegress individual stock returns on Market index returns

Best Fit Regression Line

Return

15%

10%

5%

S&P

Return

-15%

-10%

-5%

5%

10%

15%

-5%

-10%

rise

run

5.5%

5%

Slope =

= 1.1

=

-15%

Risk and Rates of ReturnRegress individual stock returns on Market index returns

Return

15%

10%

5%

S&P

Return

-15%

-10%

-5%

5%

10%

15%

-5%

-10%

-15%

Risk and Rates of Return- Market Risk is measured by Beta
- Beta is the slope of the regression (characteristic) line

Slope = 1.1 = Beta (b)

Risk and Rates of Return

- Beta is the slope of the regression (characteristic) line, i.e., 1.1 for PepsiCo
- Beta measures the relationship between the company returns and the market returns; measures non-diversifiable risk
- PepsiCo has 1.1 times (10%) more volatility than the average stock in the S & P 500, which has a slope of 1.0.(by definition)

- Market Risk is measured by Beta

Risk and Rates of Return

- Interpreting Beta

- Beta = 1

Market Beta = 1

Company with a beta of 1 has average risk

- Beta < 1

Low Risk Company

Return on stock will be less affected by the market than average

- Beta > 1

High Market Risk Company

Stock return will be more affected by the market than average

- Beta of T-Bill? = 0

The Capital Asset Pricing Model

- Investors adjust their required rates of return to compensate for risk.
- The CAPM measures required rate of return for investments, given the degree of market risk measured by beta.

The Capital Asset Pricing Model

Security Market Line

where:

Kj= required rate of return on the jth security

KRF= risk free rate of return (T-Bill)

KM= required rate of return on the market

Bj= Beta for the jth security

Km – Krf = Risk!

CAPM Example

- Suppose that the required return on the market is 12% and the risk free rate is 5%.

Security Market Line

10%

5%

Beta

.50

1.0

1.5

CAPM Example- Suppose that the required return on the market is 12% and the risk free rate is 5%.

kj = 5% + bj (12% – 5%)

Risk Free Rate

10%

5%

Beta

.50

1.0

1.5

CAPM Example- Suppose that the required return on the market is 12% and the risk free rate is 5%.

kj = 5% + bj (12% – 5%)

Risk &

Return on

market

Risk Free Rate

10%

5%

Beta

.50

1.0

1.5

CAPM Example- Suppose that the required return on the market is 12% and the risk free rate is 5%.

SML

Market

Connect Points for

Security Market Line

15%

13.4%

10%

5%

Beta

1.0 1.2

.50

1.5

CAPM ExampleSuppose that the required return on the market is 12% and the risk free rate is 5%.

If beta = 1.2

kj = 13.4

kj = 5% + bj (12% – 5%)

Market

CAPM Example

- See Table 7-4, 180, and Figure 7-7, p. 181
- Project low risk – example?
- Project average risk – example?
- Project high risk – example?
- Note: Market risk premium = Km – Krf

i.e., 12%(Km) – 4%(Krf) = 8% market risk premium

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