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Hal Varian Intermediate Microeconomics Chapter Thirteen Risky Assets.

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Presentation on theme: "Hal Varian Intermediate Microeconomics Chapter Thirteen Risky Assets."— Presentation transcript:

1 Hal Varian Intermediate Microeconomics Chapter Thirteen Risky Assets

2 Mean of a Distribution u A random variable (r.v.) w takes values w 1,…,w S with probabilities 1,..., S ( 1 + · · · + S = 1). u The mean (expected value) of the distribution is the av. value of the r.v.;

3 Variance of a Distribution u The distributions variance is the r.v.s av. squared deviation from the mean; u Variance measures the r.v.s variation.

4 Standard Deviation of a Distribution u The distributions standard deviation is the square root of its variance; u St. deviation also measures the r.v.s variability.

5 Mean and Variance Probability Random Variable Values Two distributions with the same variance and different means.

6 Mean and Variance Probability Random Variable Values Two distributions with the same mean and different variances.

7 Preferences over Risky Assets u Higher mean return is preferred. u Less variation in return is preferred (less risk).

8 Preferences over Risky Assets u Higher mean return is preferred. u Less variation in return is preferred (less risk). u Preferences are represented by a utility function U(, ). u U as mean return. u U as risk.

9 Preferences over Risky Assets Preferred Higher mean return is a good. Higher risk is a bad. Mean Return, St. Dev. of Return,

10 Preferences over Risky Assets Preferred Higher mean return is a good. Higher risk is a bad. Mean Return, St. Dev. of Return,

11 Preferences over Risky Assets u How is the MRS computed?

12 Preferences over Risky Assets u How is the MRS computed?

13 Preferences over Risky Assets Mean Return, St. Dev. of Return, Preferred Higher mean return is a good. Higher risk is a bad.

14 Budget Constraints for Risky Assets u Two assets. u Risk-free assets rate-or-return is r f. u Risky stocks rate-or-return is m s if state s occurs, with prob. s. u Risky stocks mean rate-of-return is

15 Budget Constraints for Risky Assets u A bundle containing some of the risky stock and some of the risk-free asset is a portfolio. u x is the fraction of wealth used to buy the risky stock. u Given x, the portfolios av. rate-of- return is

16 Budget Constraints for Risky Assets x = 0 and x = 1

17 Budget Constraints for Risky Assets x = 0 and x = 1 Since stock is risky and risk is a bad, for stock to be purchased must have

18 Budget Constraints for Risky Assets x = 0 and x = 1 Since stock is risky and risk is a bad, for stock to be purchased must have So portfolios expected rate-of-return rises with x (more stock in the portfolio).

19 Budget Constraints for Risky Assets u Portfolios rate-of-return variance is

20 Budget Constraints for Risky Assets u Portfolios rate-of-return variance is

21 Budget Constraints for Risky Assets u Portfolios rate-of-return variance is

22 Budget Constraints for Risky Assets u Portfolios rate-of-return variance is

23 Budget Constraints for Risky Assets u Portfolios rate-of-return variance is

24 Budget Constraints for Risky Assets u Portfolios rate-of-return variance is

25 Budget Constraints for Risky Assets Variance so st. deviation

26 Budget Constraints for Risky Assets x = 0 and x = 1 Variance so st. deviation

27 Budget Constraints for Risky Assets x = 0 and x = 1 Variance so st. deviation So risk rises with x (more stock in the portfolio).

28 Budget Constraints for Risky Assets Mean Return, St. Dev. of Return,

29 Budget Constraints for Risky Assets Mean Return, St. Dev. of Return,

30 Budget Constraints for Risky Assets Mean Return, St. Dev. of Return,

31 Budget Constraints for Risky Assets Budget line Mean Return, St. Dev. of Return,

32 Budget Constraints for Risky Assets Budget line, slope = Mean Return, St. Dev. of Return,

33 Choosing a Portfolio Budget line, slope = Mean Return, St. Dev. of Return, is the price of risk relative to mean return.

34 Choosing a Portfolio Budget line, slope = Where is the most preferred return/risk combination? Mean Return, St. Dev. of Return,

35 Choosing a Portfolio Budget line, slope = Where is the most preferred return/risk combination? Mean Return, St. Dev. of Return,

36 Choosing a Portfolio Budget line, slope = Where is the most preferred return/risk combination? Mean Return, St. Dev. of Return,

37 Choosing a Portfolio Budget line, slope = Where is the most preferred return/risk combination? Mean Return, St. Dev. of Return,

38 Choosing a Portfolio Budget line, slope = Where is the most preferred return/risk combination? Mean Return, St. Dev. of Return,

39 Choosing a Portfolio u Suppose a new risky asset appears, with a mean rate-of-return r y > r m and a st. dev. y > m. u Which asset is preferred?

40 Choosing a Portfolio u Suppose a new risky asset appears, with a mean rate-of-return r y > r m and a st. dev. y > m. u Which asset is preferred? u Suppose

41 Choosing a Portfolio Budget line, slope = Mean Return, St. Dev. of Return,

42 Choosing a Portfolio Budget line, slope = Mean Return, St. Dev. of Return,

43 Choosing a Portfolio Budget line, slope = Mean Return, St. Dev. of Return,

44 Choosing a Portfolio Budget line, slope = Higher mean rate-of-return and higher risk chosen in this case. Mean Return, St. Dev. of Return,

45 Measuring Risk u Quantitatively, how risky is an asset? u Depends upon how the assets value depends upon other assets values. u E.g. Asset As value is $60 with chance 1/4 and $20 with chance 3/4. u Pay at most $30 for asset A.

46 Measuring Risk u Asset As value is $60 with chance 1/4 and $20 with chance 3/4. u Asset Bs value is $20 when asset As value is $60 and is $60 when asset As value is $20 (perfect negative correlation of values). u Pay up to $40 > $30 for a mix of assets A and B.

47 Measuring Risk u Asset As risk relative to risk in the whole stock market is measured by

48 Measuring Risk u Asset As risk relative to risk in the whole stock market is measured by where is the markets rate-of-return and is asset As rate-of-return.

49 Measuring Risk u asset As return is not perfectly correlated with the whole markets return and so it can be used to build a lower risk portfolio.

50 Equilibrium in Risky Asset Markets u At equilibrium, all assets risk- adjusted rates-of-return must be equal. u How do we adjust for riskiness?

51 Equilibrium in Risky Asset Markets u Riskiness of asset A relative to total market risk is A. u Total market risk is m. u So total riskiness of asset A is A m.

52 Equilibrium in Risky Asset Markets u Riskiness of asset A relative to total market risk is A. u Total market risk is m. u So total riskiness of asset A is A m. u Price of risk is u So cost of asset As risk is p A m.

53 Equilibrium in Risky Asset Markets u Risk adjustment for asset A is u Risk adjusted rate-of-return for asset A is

54 Equilibrium in Risky Asset Markets u At equilibrium, all risk adjusted rates- of-return for all assets are equal. u The risk-free assets = 0 so its adjusted rate-of-return is just u Hence, for every risky asset A.

55 Equilibrium in Risky Asset Markets u That at equilibrium in asset markets is the main result of the Capital Asset Pricing Model (CAPM), a model used extensively to study financial markets.


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