Booth+Cleary+R

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As a rough measure of risk, range tells us that common stock is more risky than treasury bills.
4th – Edition Chapter 8 Concepts
Differences in Levels of Risk



While past returns might be interesting, investor’s are most concerned with future returns. Sometimes, historical average returns will not be realized in the future. Developing an independent estimate of ex ante returns usually involves use of forecasting discrete scenarios with outcomes and probabilities of occurrence.
Illustrated
Outcomes that produce harm
Probability
The wider the range of probable outcomes the greater the risk of the investment.
B
A is a much riskier investment than B
Key Chapter Concepts
Chapter 8 – Return, Risk and Portfolio Theory Measuring Ex Ante Returns
Prepared by
Ken Hartviksen
4th Edition
Ex Ante Returns and Risk
A
-30% -20%
-10%
0%
10% 20% 30% 40% Possible Returns on the Stock
4th – Edition Chapter 8 Concepts
Refining the Measurement of Risk
Standard Deviation (σ)


(The following two slides show the two different formula used for Standard Deviation)
4th – Edition Chapter 8 Concepts
Measuring Risk
Ex post Standard Deviation
(3) (4)=(2)×31) Possible Weighted Returns on Possible Probability of Stock A in that Returns on State of the Economy Occurrence State the Stock Economic Expansion 25.0% 30% 7.50% Normal Economy 50.0% 12% 6.00% Recession 25.0% -25% -6.25% Expected Return on the Stock = 7.25%
i 1
n
Where:
ER = the expected return on an investment Ri = the estimated return in scenario i Probi = the probability of state i occurring
4th – Edition Chapter 8 Concepts
(1)
(2)
Estimating Expected Returns
Estimating Ex Ante Returns Using a Formula Approach
Example Solution: Sum the products of the probabilities and possible returns in each state of the economy.
ExpectedReturn (ER) (ri P robi )
i 1
n
(r1 P rob 1 ) (r2 P rob 2 ) (r3 P rob 3) (30% 0.25) (12% 0.5) (-25% 0.25) 7.25%
Measuring Risk
Range measures risk based on only two observations (minimum and maximum value) Standard deviation uses all observations.

Standard deviation can be calculated on forecast or possible returns as well as historical or ex post returns.
- Associated probabilities for those possible returns
Possible Returns on Security A -22.0% 14.0% 35.0%
State of the Economy Recession Normal Economic Boom
Estimating Expected Returns
Estimating Ex Ante (Forecast) Returns Using a Spreadsheet Approach
Example Solution: Sum the products of the probabilities and possible returns in each state of the economy.
Estimating Expected Returns
Estimating Ex Ante (Forecast) Returns
Example: This is type of forecast data that are required to make an ex ante estimate of expected return.
[8-7]
Ex post
2 ( r r ) i i 1
n
_
n 1
Where : t hest andarddeviat ion r t heaverageret urn ri t heret urnin year i n t he number of observat io ns
Historical Nominal 10 Returns
(1957-2010) 8 (%)
S&P/TSX Bonds T-bill
6
4 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Risk – Standard Deviation (%)
Measuring Expected (Ex Ante) Returns
4th – Edition Chapter 8 Concepts
Estimating Expected Returns
Estimating Ex Ante (Forecast) Returns

The general formula
ExpectedReturn (ER) (ri Probi )
Risk, Return and Portfolio Theory
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.
4th – Edition Chapter 8 Concepts
Risk
Illustrated
Probability
Outcomes that produce harm
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.
State of the Economy Economic Expansion Normal Economy Recession
Probability of Occurrence 25.0% 50.0% 25.0%
Possible Returns on Stock A in that State 30% 12% -25%
Historical Asset Class Returns
Nominal Returns of Asset Classes
1957-2010 (in %) AM = GM = Standard Deviation = Number of years of data = CPI 3.98 3.94 3.15 54 T-bill 6.39 6.32 3.84 54 Bonds S&P/TSX 7.87 10.74 7.59 9.37 7.99 17.03 54 54