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REAUZED RATES OF RETURN Stocks A and B have the following historical returns: Year Stock A’s Returns, r A Stock B’s Returns, r B 2009 (18.00%) (14.50%) 2010 33.00 21.80 2011 15.00 30.50 2012 (0.50) (7.60) 2013 27.00 26.30 a. Calculate the average rate of return for each stock during the period 2009 through 2013. b. Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would the realized rate of return on the portfolio have been each year? What would the average return on the portfolio have been during this period? c. Calculate the standard deviation of returns for each stock and for the portfolio. d. Calculate the coefficient of variation for each stock and for the portfolio. e. Assuming you arc a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why?
Fundamentals of Financial Manageme...
Solutions
Fundamentals of Financial Manageme...
REAUZED RATES OF RETURN Stocks A and B have the following historical returns:
| Year | Stock A’s Returns, rA | Stock B’s Returns, rB |
| 2009 | (18.00%) | (14.50%) |
| 2010 | 33.00 | 21.80 |
| 2011 | 15.00 | 30.50 |
| 2012 | (0.50) | (7.60) |
| 2013 | 27.00 | 26.30 |
- a. Calculate the average rate of return for each stock during the period 2009 through 2013.
- b. Assume that someone held a portfolio consisting of 50% of Stock A and 50% of Stock B. What would the realized rate of return on the portfolio have been each year? What would the average return on the portfolio have been during this period?
- c. Calculate the standard deviation of returns for each stock and for the portfolio.
- d. Calculate the coefficient of variation for each stock and for the portfolio.
- e. Assuming you arc a risk-averse investor, would you prefer to hold Stock A, Stock B, or the portfolio? Why?
a.
To determine: The average rate of return for each stock during the given period.
Portfolio:
The portfolio refers to a group of financial assets like bonds, stocks, and equivalents of cash. The portfolio is held by investors and financial users. A portfolio is constructed based on the risk tolerance and the objectives of the company.
The Required Rate of Return:
The required rate of return is the rate, which should be minimum earned on an investment to keep that investment running in the market. When the required return is earned, only then the users and the companies invest in that particular investment.
Explanation of Solution
Calculate the average rate of return for both of the stock.
The formula to calculate the average rate of return is,
Calculation of the average rate of return for stock A:
Substitute (18%), 33%, 15%, (0.5%) and 27% for value of stock A and 5 for the number of stocks in the above formula.
b.
To determine: The realized rate of return on the portfolio for each year and the average return on portfolio for the given assumptions.
c.
To determine: The standard deviation of returns for each stock and for the portfolio.
d.
To determine: The coefficient of variation for each stock and for the portfolio.
The Coefficient of Variation:
The coefficient of variation is a tool to determine the risk. It determines the risk per unit of return. It is used for measurement when the expected returns are same for two data.
e.
To determine: The stock or the portfolio to be chosen and the reason for it.
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