Intermediate Microeconomics · free preview

Risky Assets and Portfolio Choice

Portfolio risk and return combine linearly when mixing a riskless and a risky asset, drawing a budget line in standard-deviation versus mean space whose slope prices risk, and risk-averse preferences pick the tangency.

1. Measuring a risky asset

Measuring a risky asset

2. The portfolio line

The portfolio line

3. Choosing the tangency

Choosing the tangency

4. Applications of the line

Applications of the line

5. The portfolio mean

Riskless 3 percent, risky mean 9 percent, half of wealth in each. What is the portfolio's expected return?

6. The portfolio deviation

Same half-half portfolio with risky deviation 18 percent. What is its standard deviation?

7. The price of risk

With riskless 3, market mean 9, market deviation 18, what is the slope of the risk budget line and what does it say?

8. Leveraging beyond the market

An investor puts 150 percent of wealth in the risky asset, borrowing 50 percent at the riskless rate. Where does she sit?

9. The deviation taken

With market deviation 18 percent, compute the portfolio deviation at risky share 0.25, and write the number in percent.

10. The mean earned there

Same share, riskless 3 and risky mean 9, compute the portfolio mean in percent, and write the number.

11. All in on risk

An investor puts her whole wealth in the risky asset, risky share of 1. What are the portfolio's mean and deviation?

12. Three quarters in

With risky share 0.75, what does the portfolio deliver?

13. The leveraged end

An investor borrows half her wealth at the riskless rate to hold 150 percent in the risky asset. What are the portfolio's statistics?

14. The constant price of risk

Along the whole portfolio line, what stays constant as the risky share changes?

15. Mean at three quarters

With riskless 3 and risky mean 9 percent, compute the portfolio mean at risky share 0.75, and write the number in percent.

16. Deviation under leverage

With risky deviation 18 percent, compute the portfolio deviation at risky share 1.5, and write the number in percent.

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