# Financial Problems Slide

**Topics:**Investment, Capital asset pricing model, Standard deviation

**Pages:**15 (1566 words)

**Published:**December 3, 2012

Chapter 5

Risk and Rates of Return

FIN 254 (Instructor- Saif Rahman)

Introduction to Risk and Return

Risk and return are the two most important attributes of an investment. Research has shown that the two are linked in the capital markets and that generally, higher returns can only be achieved by taking on greater risk. Risk isn’t just the potential loss of return, it is the potential loss of the entire investment itself (loss of both principal and interest). Consequently, taking on additional risk in search of higher returns is a decision that should not be taking lightly. 1

FIN 254 (Instructor- Saif Rahman)

There is a risk-return trade-off. Increasing return requires bearing more risk. Reducing risk means sacrificing return. 2

FIN 254 (Instructor- Saif Rahman)

Expected Rate of return

The rate of return expected to be realized from an investment.

Company

Expected Rate of Return

Probability

IBM

-22% -2 20 35 50

10% 20 40 20 10

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FIN 254 (Instructor- Saif Rahman)

Return: Calculating the expected return for each alternative k expected rate of return k k i Pi

i 1 ^ ^ n ^

k IBM (-22%) (0.1) (-2%) (0.2) (20%) (0.4) (35%) (0.2) (50%) (0.1) 17.4% 4

FIN 254 (Instructor- Saif Rahman)

Summary of expected returns for all alternatives

IBM Market USR T-bill Shell

Exp return 17.4% 15.0% 13.8% 8.0% 1.7%

IBM has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?

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FIN 254 (Instructor- Saif Rahman)

Risk

Probability of incurring harm

For investors, risk is the probability of earning an inadequate return.

If investors require a 10% rate of return on a given investment, then any return less than 10% is considered harmful.

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FIN 254 (Instructor- Saif Rahman)

Risk

Illustrated

Probability

The range of total possible returns on the stock A runs from -30% to more than +40%. If the required return on the stock is 10%, then those outcomes less than 10% represent risk to the investor.

Outcomes that produce harm

A

-30% -20%

-10%

0%

10% 20% 30% 40% Possible Returns on the Stock

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FIN 254 (Instructor- Saif Rahman)

Risk: Calculating the standard deviation for each alternative Standard deviation

Variance 2

ˆ)2 Pi (k i k

i1

n

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FIN 254 (Instructor- Saif Rahman)

Standard deviation calculation

i 1

n

(k i k ) 2 Pi

^

(-22.0 - 17.4) (0.1) (-2.0 - 17.4) (0.2) 2 2 IBM (20.0 - 17.4) (0.4) (35.0 - 17.4) (0.2) (50.0 - 17.4)2 (0.1) 2 2

1

2

IBM 20.04% T -bills 0.0%

9

Shell 13.4% USR 13.8% M 15.3%

FIN 254 (Instructor- Saif Rahman)

What is investment risk?

Typically, investment returns are not known with certainty. Investment risk pertains to the probability of earning a return less than that expected. The greater the chance of a return far below the expected return, the greater the risk. Two types of investment risk

Stand-alone risk Portfolio risk

Stand-alone risk: The risk an investor would face if he or she held only one asset. Portfolio risk: The riskiness of assets held in portfolios.

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FIN 254 (Instructor- Saif Rahman)

Comments on standard deviation as a measure of risk

Standard deviation (σi) measures total, or stand-alone, risk.

The larger σi is, the lower the probability that actual returns will be closer to expected returns. Difficult to compare standard deviations, because return has not been accounted for.

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FIN 254 (Instructor- Saif Rahman)

Comparing risk and return

Security Expected return Risk, σ

T-bills IBM

8.0% 17.4%

0.0% 20.04%

Shell

USR

1.7%

13.8%

13.4%

13.8%

Market

15.0%

15.3%

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FIN 254 (Instructor- Saif...

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