Portfolio Theory
Financial Investments
Fall 2012
Joni Kokkonen
General outline
1. “Technological” part of asset allocation
– How can we characterize the opportunities available to the investor given the features of the broad asset markets in which they can invest? – The investment opportunity set
2. “Personal” part of asset allocation
– How should an individual investor choose the best risk-return combination from the set of feasible combinations?
3. Equilibrium
– When all investors optimize their portfolios, how are asset returns determined in equilibrium?
Agenda
• • • • • Risk, risk aversion, and utility Portfolio risk and return Diversification Allocation between one risky and a risk-free asset Optimal risky portfolios and the efficient frontier
“OCTOBER: This is one of the peculiarly dangerous months to speculate in stocks in. The other are July, January, September, April, November, May, March, June, December, August, and February.” (Mark Twain)
Key ideas of portfolio theory
• Risk of a single investment vs. the new investment as part of one’s existing portfolio? • Diversification = “Don't put all your eggs in one basket” • Finding the least risky portfolio for any level of target return • Finding the portfolio with the highest expected return for any level of target risk • Assessing the risk-return relationship of various investments • Selecting an optimal portfolio
Practical value
Asset management • Asset allocation • Portfolio optimization • Performance measurement Risk management • Scenario analysis • Value-at-Risk (VaR) Banking • Credit risk pricing
Risk aversion
• Assume we want to invest 100 000 and have two possible investment strategies:
1. A risky investment giving a profit of 50 000 with probability 0.6 and a loss of 20 000 with a probability 0.4 2. A risk-free investment giving a profit of 5000
• The expected profit from the risky strategy is 22 000 • The incremental profit of the risky strategy over the riskfree
Fall 2012
Joni Kokkonen
General outline
1. “Technological” part of asset allocation
– How can we characterize the opportunities available to the investor given the features of the broad asset markets in which they can invest? – The investment opportunity set
2. “Personal” part of asset allocation
– How should an individual investor choose the best risk-return combination from the set of feasible combinations?
3. Equilibrium
– When all investors optimize their portfolios, how are asset returns determined in equilibrium?
Agenda
• • • • • Risk, risk aversion, and utility Portfolio risk and return Diversification Allocation between one risky and a risk-free asset Optimal risky portfolios and the efficient frontier
“OCTOBER: This is one of the peculiarly dangerous months to speculate in stocks in. The other are July, January, September, April, November, May, March, June, December, August, and February.” (Mark Twain)
Key ideas of portfolio theory
• Risk of a single investment vs. the new investment as part of one’s existing portfolio? • Diversification = “Don't put all your eggs in one basket” • Finding the least risky portfolio for any level of target return • Finding the portfolio with the highest expected return for any level of target risk • Assessing the risk-return relationship of various investments • Selecting an optimal portfolio
Practical value
Asset management • Asset allocation • Portfolio optimization • Performance measurement Risk management • Scenario analysis • Value-at-Risk (VaR) Banking • Credit risk pricing
Risk aversion
• Assume we want to invest 100 000 and have two possible investment strategies:
1. A risky investment giving a profit of 50 000 with probability 0.6 and a loss of 20 000 with a probability 0.4 2. A risk-free investment giving a profit of 5000
• The expected profit from the risky strategy is 22 000 • The incremental profit of the risky strategy over the riskfree