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Unformatted text preview: Expected Rates of Return
• • In previous examples, we discussed
realized historical rates of return. In
contrast, an investor would be more
interested in the expected return on a
future risky investment.
Risk refers to the uncertainty of the future
outcomes of an investment
– – There are many possible returns/outcomes
from an investment due to the uncertainty
11
Probability is the likelihood of an outcome Expected Rates of Return
• Computing Expected Rate of Return
n E(R i ) = ∑ (Probabilit y of Return) × (Possible Return)
i =1 = [(P1 )(R 1 ) + (P2 )(R 2 ) + .... + (Pn R n )]
n = ∑( Pi )( Ri )
i =1 where P i = Probability for possible return i
12 Probability Distributions
Exhibit 1.2
Riskfree Investment
1.00
0.80
0.60
0.40
0.20
0.00 5% 0% 5% 10% 15%
13 Probability Distributions
Exhibit 1.3
Risky Investment with 3 Possible
Returns
1.00
0.80
0.60
0.40
0.20
0.00 30% 10% 10% 30%
14 Probability
Distributions
Exhibit 1.4
Risky investment with ten possible
returns
1.00
0.80
0.60
0.40
0.20
0.00
40% 20% 0% 20% 40%
15 Risk of Expected Return
• • • Risk refers to the uncertainty of an
investment; therefore the measure of risk
should reflect the degree of the
uncertainty.
The risk of expected return reflects the
degree of uncertainty that actual return will
be different from the expected return.
The common measures of risk are based
16
on the variance of the rates of return Risk of Expected Return
• Measuring the Risk of Expected Return
– The Variance Measure
Variance (σ )
n Possible Expected 2
= ∑ (Pr obability ) x (
−
)
Re turn
Re turn
i= 1
= n Pi [ Ri − E ( Ri )]2
∑
i= 1 17 Risk of Expected Return
Standard Deviation (σ): It is the square root
of the variance and measures the total risk – σ=
– n − E ( Ri )]2
∑ Pi [ Ri
i= 1 Coefficient of Variation (CV): It measures the risk
per unit of expected return and is a relative
measure of risk.
Standard Deviation of Return
Expected Rate of Return
=σ
E (R) CV = 18 ...
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 Spring '12
 DAVIDBRAY
 Interest

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