1. Intensive Actuarial Training for Bulgaria January 2007 Lecture 16 – Portfolio Optimization and Risk Management By Michael Sze, PhD, FSA, CFA

2. Financial Planning Process Aim: To match financial needs to resources on long term and short term bases Steps –Know your client: needs, income, –Planned events: education, major purchases, retirement –Contingent events: death, sickness, job loss, divorce –Projected cashflow until the younger spouse is 100 years old Graphs, what ifs: different investment returns, pay increases

3. Determinants of the Required Rate of Return Real risk free rate Expected inflation rate premium Risk premium

4. Nominal Risk-Free Rate Expected Inflation = 4% Real Rate = 2% Nominal Rate = 2% + 4% = 6% This is the approximation method. The correct method is: (1 + real risk free rate)(1 + inflation rate) – 1 [1.02 × 1.04] – 1 = 6.08%

5. Risk Premium Factors Business risk Financial risk Liquidity risk Exchange rate risk Country risk

6. Life Cycle of Wealth Accumulation Consolidation Spending Gifting

7. Portfolio Management Policy statement Investment strategy Implementation Monitor & rebalance

8. Policy Statement The roadmap that guides the investment process It forces investors to understand and articulate their needs and constraints Sets performance standards and specifies benchmarks Imposes investment discipline on the client and the portfolio manager

9. Objectives Risk tolerance Return objectives

10. Constraints Time horizon Liquidity needs Taxes Legal/regulatory Unique needs

11. Asset Allocation Which asset classes will be allowed in the portfolio? (policy) What is the normal weighting for each asset class? (policy) How far can we deviate from the stated policy? (timing) What specific securities will be purchased for the portfolio? (selection)

12. Asset Allocation Equities are riskier but need to be represented in a significant way in the portfolio to preserve capital value over long time periods Over long periods government securities are less volatile than equities. Asset allocation can help reduce the volatility of a portfolio’s returns.

13. Risk Aversion Prefers higher return for same level of risk Prefers lower risk for same level of return

14. Measures of Risk The most common measure of risk used in finance is variance and standard deviation which is the square root of the variance Alternative measures of risk include the range and semivariance You should be able to calculate variance with both expectational and historical data

17. Standard Deviation of a Portfolio  2 =(0.4) 2 (0.2) 2 + (0.6) 2 (0.28) 2 + 2 (0.4) (0.6) (0.2) (0.28) (0.6) = 0.051 = [0.051] 1/2 = 22.58% Note that the standard deviation of the two stock portfolio is less than the weighted average of the two standard deviations [(0.4 × 0.2) + (0.6 × 0.28)] = 24.8%

19. Expected Return and Standard Deviation of a Portfolio The expected return of the portfolio is the weighted average return of the individual assets The standard deviation of the portfolio is less than the weighted average standard deviation as long as the correlation coefficient is less than +1

20. The Development of the Efficient Frontier Markowitz realized that we can create portfolios with the same level of risk and higher rates of return, or the same level of return and lower levels of risk, by diversifying our investments across many stocks The lower the correlation coefficient (the closer it is to negative 1), the greater the benefits of diversification

21. Efficient Frontier A portfolio is efficient if no other portfolio offers a higher level of expected return with the same or lower risk. Alternatively, no other portfolio offers lower risk for the same or higher return. The efficient frontier and the concept of efficient portfolios is the key concept in portfolio theory and capital market theory

23. Optimal Portfolio on a Efficient Frontier Steep indifference curves imply a highly risk averse investor while flatter indifference curves imply less risk aversion The investor’s optimal portfolio lies where the efficient frontier is tangent to the highest indifference curve