Investment Portfolio And Stock Return Analysis

Problem;

Suppose you invest $400,000 in Treasury bills and $600,000 in the market portfolio. What is the return on your portfolio if bills yield 3% and the expected return on the market is 10%? What does the return on this portfolio imply for the expected return on individual stocks with betas of .6?

Let's break this down into two parts:

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Part 1: Portfolio Return Calculation

You invested:

• $400,000 in Treasury bills (risk-free asset) yielding 3%

• $600,000 in the market portfolio with an expected return of 10%

The return on the total portfolio is the weighted average of these two:

$$\text{Portfolio Return} = (w_{\text{bills}} \times R_f) + (w_{\text{market}} \times R_m)$$

Where:

• $R_f = 3\%$
  

• $R_m = 10\%$
  

• $w_{\text{bills}} = \frac{400,000}{1,000,000} = 0.4$
  

• $w_{\text{market}} = \frac{600,000}{1,000,000} = 0.6$
  

$$\text{Portfolio Return} = (0.4 \times 0.03) + (0.6 \times 0.10) = 0.012 + 0.06 = 0.072 = \boxed{7.2\%}$$

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Part 2: Expected Return on Individual Stocks with Beta = 0.6

We use the Capital Asset Pricing Model (CAPM):

$$E(R_i) = R_f + \beta_i (R_m - R_f)$$

Where:

• $R_f = 3\%$
  

• $R_m = 10\%$
  

• $\mathrm{<span\; style="font-size:\; medium;"><b>\beta </b></span>}<span\; style="font-size:\; medium;"><b>=</b></span>\mathrm{<span\; style="font-size:\; medium;"><b>0.6</b></span>}$

$$E(R_i) = 0.03 + 0.6 \times (0.10 - 0.03) = 0.03 + 0.6 \times 0.07 = 0.03 + 0.042 = \boxed{7.2\%}$$

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Conclusion

• Your portfolio return is 7.2%.

• A stock with a beta of 0.6 also has an expected return of 7.2%.

This means your portfolio has the same systematic risk (beta = 0.6) as a stock with beta 0.6, and under CAPM assumptions, you'd expect the same return—showing consistency between the portfolio's composition and the expected return for assets with similar risk.