Question

< 0.55 21. Your portfolio has a beta of 1.18. The portfolio consists of $3000 in U.S. Treasury bills, $8000 in stock A, and $5500 in stock B. Stock A has a risk-level equivalent to that of the overall market. What is the beta of stock B? 0 Find Total value of portfolio: 1.10 1.24 8000 + 5500 + 3000 = 16, SOO 1.85 2.09 o் ③ Beta portfolio = 1.18= 10 x 3000 16,500) + (1x8000 TES

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Answer 1

Option (e) is correct

Portfolio beta is the weighted average beta of the stocks in the portfolio. U.S. Treasury bills has zero beta. Stock A has beta equivalent to market beta. Market beta is always 1. So, stock A has a beta of 1.

Calculation of beta of stock B:

In the first step, we will calculate the weight of each stock by dividing the amount invested in each stock by the total amount the amount invested in the fund i.e. $3000 + $8000 + $5500 = $16500.:

US Treasury (w1): $3000 / $16500 = 0.181818

Stock A (w2): $8000 / $16500 = 0.484848

Stock B (w3): $5500 / $16500 = 0.3333

In the next step we will use the formula of weighted average beta to calculate the beta of stock B.

Weighted average beta = w1 * b1 + w2 * b2 + w3 * b3

where, w1,w2,w3 are the weights of stocks and b1,b2,b3 are the respective beta of stocks.

Putting the values in the above formula, we get,

1.18 = (0.1818 * 0) + (0.4848 * 1) + (b2 * 0.3333)

1.18 = 0 + 0.4848 + 0.3333* b2

1.18 - 0.4848 = 0.3333 * b2

0.6952 = 0.3333 * b2

b2 = 0.6952 / 0.3333

b2 = 2.09

So, beta of stock B is 2.09