✏️ Examples (CAPM)
✏️ You are considering investing in two portfolios: A and B:
What is the standard deviation of portfolio B and the covariance between A and B?
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✏️ Suppose you invest in portfolio A and in portfolio B. What is the Expected return, variance, standard deviation, risk premium, and Sharpe ratio of the resulting portfolio?
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✏️ You are considering investing in a stock. Its current price is $78 and you expect that next year it will pay a dividend of $3 and have a price of $85. It has a of . and . Is this stock overpriced or underpriced?
Note: for a discussion of questions like this, see: ✏️ CAPM, Dividends, and Holding Period Return
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We have the tools to calculate HPR and to calculate what the CAPM says a fair return would be. Let’s calculate both and then compare them to see whether the stock is overpriced or underpriced.
The stock “should” have a return of 11.8%, but it actually will have a return of 13%. The only way for it to have a return this high is if it is currently underpriced and is currently a good deal. Underpriced. It has an alpha of
✏️ Consider the above stock. If it is currently underpriced, what would a fair price for it be?
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We have equations that connect up all of the relevant variables, so let’s just “Plug and Chug.”
Plug and chug: (help)
- Equation:
- Plug:🔌
- Solve: 🚂
- Reflect: 🧠
We think that the stock should be _$78.71_ right now. Earlier, when was $78.00, the stock was underpriced and the HPR was 13%, which was higher than the CAPM suggested. Now, at the higher price of $78.71, it’s not quite as good of a deal and only has an HPR of 11.8%, in line with the CAPM’s prediction.
✏️ In the previous problem, we assumed that the market was wrong about the current price of the stock - ie that the stock was underpriced. Let’s instead consider that perhaps our projection of the future price ($85) is incorrect. Based on the actual current price fo the stock and on CAPM’s prediction of , what future price would you predict for the stock? In other words, what would the future stock price have to be to give the stock an 11.8% return?
✏️ Given the numbers we’ve discussed before, would an Expected Return of 14% for this stock be consistent with the CAPM?
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We know that , and from above.
Based on this, the CAPM implies that
This is not consistent with having an expected return of .