Question
In: Finance
You want to create a portfolio equally as risky as the market, and you have $1,000,000...
|
You want to create a portfolio equally as risky as the market, and you have $1,000,000 to invest. Consider the following information: |
| Asset | Investment | Beta |
| Stock A | $200,000 | 0.85 |
| Stock B | $350,000 | 1.20 |
| Stock C | 1.55 | |
| Risk-free asset | ||
| Required: |
| (a) | What is the investment in Stock C? (Do not round your intermediate calculations.) |
| (Click to select)$275,097$253,935$264,516$251,290$144,849 |
| (b) | What is the investment in risk-free asset? (Do not round your intermediate calculations.) |
| (Click to select)$192,903$178,065$305,151$176,210$185,484 |
Solutions
Expert Solution
- Beta of the market is equal to one, therefore the beta of the portfolio which is equally as risky as the market will be equal to one.
And beta of risk free asset is assumed as zero.
We can use following formula to calculate the proportion of investment in stock C and risk free asset
Beta of portfolio = Beta of Stock A * weight of stock A in portfolio + Beta of Stock B * weight of stock B in portfolio + Beta of Stock C * weight of stock C in portfolio + Beta of risk free asset * weight of risk free asset in portfolio
Where,
Beta of portfolio = 1
Beta of Stock A = .85
Weight of stock A in portfolio = Investment in stock A / total investment in portfolio
= $200,000/$1,000,000 = 0.20
Beta of Stock B = 1.20
Weight of stock B in portfolio = Investment in stock B / total investment in portfolio
= $350,000/$1,000,000 = 0.35
Beta of Stock C = 1.55
Assume that investment in stock C is X, therefore
Weight of stock C in portfolio = X/ $1,000,000
Beta of risk free asset = 0
Weight of risk free asset in portfolio = ($1,000,000 - $200,000 - $350,000 –X)/$1,000,000
= ($450,000 –X) /$1,000,000
Now putting all the values into formula, we get
1 = 0.85 * 0.20 + 1.20 * 0.350 + 1.55 * (X/$1,000,000) + 0 * ($450,000 –X) /$1,000,000
Or 1 – 0.59 = 1.55 * (X/$1,000,000)
Or 0.41/1.55 = X/$1,000,000
Or X = 0.264516* $1,000,000 = $264,516
Therefore investment in stock C is $264,516
- And investment in risk free asset = $450,000 –X = $450,000 –$264,516 = $185,484
jeff jeffy answered 1 year agoRelated Solutions
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