Assignment: Investment and Risk Management

1. Chapter 7
Optimal Risky Portfolios
Group 2:
1. Desyani Safitri (122011810110)
2. Kusnul Fitriani (122011810042)

2. The Investment Decision
1. Capital allocation between the risky portfolio
and risk-free asset
2. Asset allocation across broad asset classes
3. Security selection of individual assets within
each asset class

3. Diversification and Portfolio Risk
1. Market Risk
• systematic risk or non-diversifiable risk
• arises from uncertainty in the general economy associated with conditions
such as the business cycle, interest rates, exchange rates, etc.
2. Firm Specific Risk
• non-systematic risk, unique risk, or diversifiable risk
• arises from factors directly attributable to a firm’s operations, such as its
research and development opportunities or personnel changes

4. Diversification and Portfolio Risk

5. Portfolios of Two Risky Assets
• how efficient diversification is arrived at by constructing risky portfolios which
produce the lowest possible risk for any given level of expected return.
Portfolio risk depends on the correlation between the returns of the assets in
the portfolio.
• Consider a risky portfolio consisting of two risky mutual funds: a bond fund of
long-term debt securities, denoted D, and a stock fund, denoted E.
wD = Bond weight rD = Bond return E(rp) = Portfolio return
wE = Equity weight rE = Bond return

6. Portfolios of Two Risky Assets
σ2
D = Variance of Security D
σ2
E = Variance of Security E
Cov(rD,rE)= Covariance of returns for Security D & Security E
σD = Standard deviation of returns for Security D
σE = Standard deviation of returns for Security E
ρDE = Correlation coefficient of returns

7. Example
What happens when wD > 1 and wE < 0?
In this case, portfolio strategy would call
for selling the equity fund short and
investing the proceeds of the short sale in
the debt fund.
When wD < 1 and wE > 0, this strategy
calls for selling the bond fund short and
using the proceeds to finance additional
purchases of the equity fund.

8. Example

9. Asset Allocation with Stocks, Bonds,
and Bills
• Determining the weights associated with the optimal risky portfolio
P (consisting of a stock fund and bond fund)
• Determining the optimal proportion of the complete portfolio
(consisting of an investment in the optimal risky Portfolio P and one
in a risk free component (T-Bills)) to invest in the risky component.
• If investor’s coefficient of risk aversion (A) = 4 and T-Bills (rf) = 5%

10. Asset Allocation with Stocks, Bonds,
and Bills

11. Asset Allocation with Stocks, Bonds,
and Bills

12. The Markowitz Portfolio Selection
Model
The steps involved in portfolio construction when considering the
case of many risky securities and a risk- free asset can be
generalized as follows:
Step 1: Identify the risk-return combinations available from the set
of risky assets.
Step 2: Identify the optimal portfolio of risky assets by finding the
portfolio weights that result in the steepest CAL.
Step 3: Choose an appropriate complete portfolio by mixing the risk
free asset with the optimal risky portfolio.

13. Risk Pooling, Risk Sharing, And Risk of
Long Term Investments
• Risk pooling means merging uncorrelated risky assets to reduce risk. For
insurance, risk pooling entails selling many uncorrelated insurance
policies (a.k.a. the insurance principle).
• The insurance principle: risk increases less than proportionally to the
number of policies insured when the policies are uncorrelated
- Sharpe ratio increases
• Risk Sharing As risky assets are added to the portfolio, a portion of the
pool is sold to maintain a risky portfolio of fixed size.
• Risk sharing combined with risk pooling is the key to the insurance
industry.
• True diversification means spreading a portfolio of fixed size across
many assets, not merely adding more risky bets to an ever- growing risky
portfolio.

14. Investment for the Long Run
Long Term Strategy
• “Invest in the risky portfolio
for 2 years”
• Long-term strategy is riskier.
• Risk can be reduced by
selling some of the risky
assets in year 2.
• “Time diversification” is not
true diversification.
Short Term Strategy
• “Invest in the risky portfolio
for 1 year and in the risk-
free asset for the second
year”

15. Thank You