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Keep the Highest no score out of 2/ 2

2. Statistical measures of stand-alone risk

Remember, the expected value of a probability distribution is a statistical measure of the average (mean) value expected to occur during all possible circumstances. To compute an assets expected return under a range of possible circumstances (or states of nature), multiply the anticipated return expected to result during each state of nature by its probability of occurrence.

Consider the following case:

James owns a two-stock portfolio that invests in Happy Dog Soap Company (HDS) and Black Sheep Broadcasting (BSB). Three-quarters of Jamess portfolio value consists of HDSs shares, and the balance consists of BSBs shares.

Each stocks expected return for the next year will depend on forecasted market conditions. The expected returns from the stocks in different market conditions are detailed in the following table:

Market Condition	Probability of Occurrence	Happy Dog Soap	Black Sheep Broadcasting
Strong	0.20	20%	28%
Normal	0.35	12%	16%
Weak	0.45	-16%	-20%

Calculate expected returns for the individual stocks in Jamess portfolio as well as the expected rate of return of the entire portfolio over the three possible market conditions next year.

	The expected rate of return on Happy Dog Soaps stock over the next year is .
	The expected rate of return on Black Sheep Broadcastings stock over the next year is .
	The expected rate of return on Jamess portfolio over the next year is .

The expected returns for Jamess portfolio were calculated based on three possible conditions in the market. Such conditions will vary from time to time, and for each condition there will be a specific outcome. These probabilities and outcomes can be represented in the form of a continuous probability distribution graph.

For example, the continuous probability distributions of rates of return on stocks for two different companies are shown on the following graph:

Based on the graphs information, which statement is false?

Company H has lower risk.

Company G has lower risk.

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Keep the Highest no score out of 3/ 3

3. Measuring stand-alone risk using realized (historical) data

Returns earned over a given time period are called realized returns. Historical data on realized returns is often used to estimate future results. Analysts across companies use realized stock returns to estimate the risk of a stock.

Consider the case of Falcon Freight Inc. (FF):

Five years of realized returns for FF are given in the following table. Remember:

1.	While FF was started 40 years ago, its common stock has been publicly traded for the past 25 years.
2.	The returns on its equity are calculated as arithmetic returns.
3.	The historical returns for FF for 2014 to 2018 are:

	2014	2015	2016	2017	2018
Stock return	20.00%	13.60%	24.00%	33.60%	10.40%

Given the preceding data, the average realized return on FFs stock is .

The preceding data series represents of FFs historical returns. Based on this conclusion, the standard deviation of FFs historical returns is .

If investors expect the average realized return from 2014 to 2018 on FFs stock to continue into the future, its coefficient of variation (CV) will be .

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