14
Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Embed Size (px)

Citation preview

Page 1: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Risk Aversion and Capital Allocation

Risk Tolerance

Asset Allocation

Capital Allocation Line

Page 2: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 2

Risk Premium and Risk Aversion Risk Premium: E[r] - rf

It is compensation for risk

Risk Measure*: (Std. Dev.)

Risk Aversion coeff: A

221

frrEA

][

* just one of them

Page 3: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 3

Risk Premium and Risk Aversion Example

Market portfolio E[r] = 12% Market portfolio = 20% Risk-free rate (T-bill) = 4%

Risk premium: E[r] - rf = 8% Risk aversion coefficient:

A = 0.08/(0.5*0.20^2) = 4

Page 4: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 4

Speculation vs. Gambling Speculation (i.e. Investing)

Taking risk for extra reward Higher investors’ risk aversion requires higher

expected returns

Risk premium: E[r] - rf > 0 Odds are in your favor

Gambling Risk is the reward Risk premium: E[r] - rf < 0

Odds are against you

Page 5: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 5

Asset Allocation How to allocate your fund among the

following asset classes?

Investment Funds

Stock Bond T-Bills

Risky AssetsRisk-Free Asset

Page 6: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 6

Asset Allocation Risky and Risk-Free Assets

Percentage to invest in risky asset Risky asset: a stock or a stock portfolio

Percentage in risk-free asset Risk-free asset: 30-day T-bill as proxy

Issues Examine risk/return tradeoff Demonstrate how different degrees of risk

aversion will affect allocations between risky and risk-free assets

Page 7: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 7

Asset Allocation Moments of asset returns

Moments of portfolio C return

Example: w = 0.75

wr

wrE

ff

pp

107

2215

%%Free-Risk

%%][Risky

WeightDev StdMeanAssets

ww

wrwErwrE

pc

pfc

22.0 :Dev Std

08.007.0][)1(][ :Mean

%5.1616.022.0 :Dev Std

%1313.008.007.0][ :Mean

w

wrE

c

c

Page 8: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 8

Capital Allocation Line How much in risky asset …

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

16.0%

18.0%

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0%

SD[r_c]

E[r

_c]

%][ 15prE

%7fr

%22p

Capital Allocation Line

Risky Portfolio

w = 0.75

Risk-Free Asset

Page 9: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 9

Capital Allocation Line w > 1, what does that mean?

Find the E[rc] and SD[rc] with w = 1.2

Leverage Investing 120% of wealth in risky asset Using margin borrowing Higher expected return than the risky asset Higher volatility to go with the higher return

%4.26264.022.0 :Dev Std

%6.16166.008.007.0][ :Mean

w

wrE

c

c

Page 10: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 10

Capital Allocation Line with Borrowing

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

16.0%

18.0%

20.0%

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0%

%][ 15prE

%7fr

%22p

Capital Allocation Line: Borrowing at 10% Part

Risky Portfolio

w = 1.2

Risk-Free Asset

Page 11: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 11

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

16.0%

18.0%

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0%

SD[r_c]

E[r

_c]

Capital Allocation Line Sharpe (reward-to-variability) Ratio

%15][ prE

%7fr

%22p

%22p

%8%7%15][ fp rrE

36.0%22

%8][

:Ratio Sharpe

p

fp rrES

Page 12: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 12

Capital Allocation Line Risk Tolerance and Allocation

Greater risk aversion leads to higher allocation to risk-free asset

Lower risk aversion leads to greater allocation to risky asset

Willingness to accept extremely higher risk for higher return may lead to leveraged position

Page 13: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 13

How to find your portfolio allocation?

Example 1 You desire 12% return for your portfolio:

12% = (1-w)*7%+w*15% or w = 62.5%Std. Dev. = 62.5%*22% = 13.75%

Example 2 You desire risk no more than 10% for your

portfolio:w*Std. Dev. = 10% or w = 45.45%

Return = (1-45.45%)*7%+45.45*15% = 10.64%

Page 14: Risk Aversion and Capital Allocation Risk Tolerance Asset Allocation Capital Allocation Line

Investments 8 14

Wrap-up How does risk aversion affect expected

returns? Is investment a form of gambling??? What is the Capital Allocation Line? How risk tolerance affects asset

allocation?