How to Characterize Risk and Return

Questions: 

Expected return is considered forward-looking because it denotes the compensation investors expect to receive in the future for the market risk taken (Sherman, 2011). Moreover, expected return is used to determine whether an investment is worthwhile. In other words, expected return indicates whether or not an investment will have a positive income in the future based on historical data (Finkler, 2002). 

The challenge that arise in using expected return is that the future is never guaranteed and expected return is only an estimate of future outcomes of an investment based on its historical performance (Jordan, 2014). Hence, it cannot precisely tell what the future holds or how an investment will react to different events in the future. It is dangerous to make an investment based on its expected return only, without assessing the risks characteristics of the investment.

Every investment in the market has some risk associated with it which is measured by Beta (Staff, 2017). An investor has a choice to invest in either risk free securities or securities that bear some level of risk. The allocations of these securities can be manipulated by the investor to achieve their desired level of risk. Risk free securities have zero risk (β=0) while the market portfolio has market risk (β=1) (Weaver & Weston, 2001). If for instance an investor desired that his portfolio is made up of 40% risk-free securities, and the rest (60%) is investments that bear market risk, then it can be said that the investor’s portfolio has a beta, β = 0.60.

Computational Problems: 

For the computation problems we solve the problems algebraically as well as using the Excel spreadsheet

Based on the probability and percentage of return for the three economic states in the table below, compute the expected return.

Economic State	Probability	Percentage of Return
Fast Growth	0.10	60
Slow Growth	0.50	30
Recession	0.40	-23

Solution: 

We use the Excel spreadsheet to find the expected return. Where,

The expected return =Sum of each return X probability that return

Economic State	Probability	Percentage of Return	Probability * Return
Fast Growth	0.1	60	6
Slow Growth	0.5	30	15
Recession	0.4	-23	-9.2
Expected Return			11.8 “=SUM(E6:E8)”

The expected return for the three economic states is 11.8% 

If the risk-free rate is 7 percent and the risk premium is 4 percent, what is the required return?

Solution: 

Required return = Risk free rate + Risk premium

= 7% + 4%

= 11%

Therefore, the overall required return is 11% 

Suppose that the average annual return on the Standard and Poor's 500 Index from 1969 to 2005 was 14.8 percent. The average annual T-bill yield during the same period was 5.6 percent. What was the market risk premium during these 10 years?

Solution: 

Market risk premium = Index average returm – T-bill return

= 14.8% - 5.6%

= 9.2%

Therefore, the market risk premium during these 10 years was 9.2% 

Conglomco has a beta of 0.32. If the market return is expected to be 12 percent and the risk-free rate is 5 percent, what is Conglomco's required return? Use the capital asset pricing model (CAPM) to calculate Conglomco's required return.

Solution: 

The formula provided by the CAPM to calculate expected return is:

Expected return = r f + β (r m – r f )

Where,

r f is the risk-free rate = 5%

r m is the market return = 12%

β is the beta = 0.32

Therefore,

Expected return = 5% + 0.32 (12% - 5%) = 5% + 2.24% = 7.24%

Conglomco's required return is 7.24% 

Calculate the beta of a portfolio that includes the following stocks:

Conglomco stock, which has a beta of 3.9 and comprises 35 percent of the portfolio.

Supercorp stock, which has a beta of 1.7 and comprises 25 percent of the portfolio.

Megaorg stock, which has a beta of 0.3 and comprises 40 percent of the portfolio.

Solution: 

We use the Excel spreadsheet to find the beta of the portfolio. Where,

The beta of the portfolio = sum of each stock’s beta * weight of the stock in the portfolio

Stock	Beta	Weight in Portfolio	Beta * Weight
Conglomco	3.9	35%	1.365
Supercorp	1.7	25%	0.425
Megaorg	0.3	40%	0.12
Expected Return			1.91 “=SUM(E6:E8)”

Therefore, the beta of a portfolio is 1.91 

References 

Finkler, S. (2002).  Finance & accounting for nonfinancial managers . Paramus: Prentice Hall Press.

Jordan, B. (2014).  Fundamentals of investments . McGraw-Hill Higher Education.

Sherman, E. H. (2011). Finance and accounting for nonfinancial manager s (3rd ed.). New York, NY: American Management Association.

Staff, I. (2017).  Market Portfolio .  Investopedia . Retrieved 10 November 2017, from https://www.investopedia.com/terms/m/market-portfolio.asp 

Weaver, S. C., & Weston, J. F. (2001). Finance and accounting for nonfinancial managers . New York, NY: McGraw-Hill.