Portfolio Management Financial Markets, Day 4, Class 1 Jun Pan - PowerPoint PPT Presentation

Portfolio Management Financial Markets, Day 4, Class 1 Jun Pan Shanghai Advanced Institute of Finance (SAIF) Shanghai Jiao Tong University April 21, 2019 Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 1 / 52

Outline for Day 4 Class 1: Portfolio Management. Class 2: Risk Management. Class 3: Chinese Stock Market. Class 4: Chinese Bond Market. Class 5: Financial Institutions in China. Class 6: Review and quiz. Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 2 / 52

Outline for Class 1 The process of portfolio management. Optimal portfolio selection with one risky asset. The Optimal risky portfolio. Limitations of portfolio theory. The Black-Litterman asset allocation model. Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 3 / 52

Policy Portfolio, Harvard Management Company, 2002 Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 4 / 52

The Process of Portfolio Management Objectives of the Portfolio: Client Risk Tolerance Universe of Assets Passive vs. Active Stock Selections vs. Asset Allocation Tactical vs. Strategic Asset Allocation Selection of Benchmark Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 5 / 52

Tactical Asset Allocation Switching between asset classes Enhanced Indexing Market Timing Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 6 / 52

Security Selection within Asset Class Selection of Individual Stocks Top-Down vs. Bottom-up Growth vs. Value (“Style”) Fundamental vs. Technical Macro vs. Micro Quantitative vs. Traditional Long/Short Plays Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 7 / 52

Marketing What is your value-added? What can you promise? How do you deal with poor performance? Client services Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 8 / 52

Performance Evaluation Comparison with benchmark Risk adjustments Performance Attribution Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 9 / 52

Compensation Base + pay for performance Objective: incentive alignment High-water mark Clawback Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 10 / 52

The Investment Opportunity Monthly Returns from 198706-201009 Jun Pan Portfolio Management Financial Markets, Day 4, Class 1 0.1973 2.23% 0.77% 0.2960 1.25% 0.70% PIMCO 0.0893 5.15% 0.79% Magellan 0.1011 4.65% 0.80% CRSP VW risky asset R p NA 0 0.33% riskfree r f Sharpe ratio std mean 11 / 52 Hedge Fund Index ∗ ∗ Hedge fund data starts in 199401.

A Mean-Variance Investor 0.70% 10 -0.28% PIMCO 0.70% 1 0.69% 4 4 0.67% 0.70% 10 0.62% Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 0.80% 0.37% 12 / 52 any asset class mean variance risk aversion utility riskfree 0.33% 0.80% 0 0.33% CRSP 0.80% 1 0.69% Utility = mean − 1 2 × risk aversion × variance (4.65%) 2 (4.65%) 2 (4.65%) 2 (1.25%) 2 (1.25%) 2 (1.25%) 2

Portfolio Construction with One Risky and One Riskfree 0.1011 Assume the investor’s risk aversion = 4. He invests a fraction y of his 0.4292% 0.1011 pure risky 100% 0.80% 0.3675% 0.1011 leveraged 200% 1.27% -0.4598% short aggressive -50% 0.095% -0.0131% -0.1011 optimal 54.34% 0.59% 0.4577% 0.1011 Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 80% 0.71% 0.1011 0.3300% R p strategy y mean variance utility Sharpe ratio pure riskfree 0 0.33% 0.4569% 0 N/A 0.4067% 0.57% 50% 0.1011 half & half 0.42% 20% conservative 13 / 52 wealth in the risky asset (CRSP), and leaves 1 − y in the riskfree. ˜ R y = (1 − y ) r f + y ˜ (0.93%) 2 (2.33%) 2 (3.72%) 2 (4.65%) 2 (9.30%) 2 (2.33%) 2 (2.53%) 2

The Tradeofg of Risk and Return For any investor with a known risk aversion, we can actually solve the Adding more risky asset increases the mean of the portfolio: But it also increases the volatility of the portfolio: Recall the investor’s utility. Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 14 / 52 optimal portfolio weight y ∗ for him. mean = (1 − y ) 0 . 33 % + y 0 . 80 % = 0 . 33 % + (0 . 80 % − 0 . 33 % ) y variance = (4 . 65 % ) 2 y 2 Utility = mean − 1 2 × risk aversion × variance The optimal portfolio weight y ∗ is the portfolio mix that maximizes

The Optimal Risk and Return Tradeofg The optimal risk and return tradeofg can be achieved by: risk premium All else equal, a more risk averse investor invests less in the risky asset. All else equal, a higher risk premium induces investor to hold more of the risky asset. All else equal, a lower volatility induces investor to hold more of the risky asset. Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 15 / 52 y ∗ = variance × risk aversion

Portfolio Construction with Two Risky and One Riskfree risky asset 1 Jun Pan Portfolio Management Financial Markets, Day 4, Class 1 4.00% 0.70% risky asset 2 0.80% 5.00% 0.33% riskfree r f std mean 16 / 52 Invest a fraction w 1 in risky asset 1, w 2 in risky asset 2, and leave w 0 = 1 − w 1 − w 2 in the riskfree account: ˜ R w = w 0 r f + w 1 ˜ R 1 + w 2 ˜ R 2 . mean = w 0 × 0 . 33 % + w 1 × 0 . 80 % + w 2 × 0 . 70 % 1 × (5 . 00 % ) 2 + w 2 2 × (4 . 00 % ) 2 + 2 × w 1 × w 2 × cov. variance = w 2 cov= corr × (5 . 00 % ) × (4 . 00 % ) ; corr = 20 % .

Mean-Variance Spanned by Two Risky Assets Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 17 / 52

Portfolio Strategies and Investor Utility 1/3 0.3800% 0.0925 risky 1 & 2 60% 20% 20% 0.50% 0.4588% 0.1200 equal weight 1/3 1/3 0.61% 0.70% 0.5011% 0.1200 optimal 12.70% 39.32% 47.98% 0.69% 0.5112% 0.1204 Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan Fix risk aversion at 4: 18 / 52 100% 0.3300% strategy mean variance utility Sharpe ratio riskfree 100% 0 0 0 0 0.33% N/A 0.80% 0 all risky 2 0.0940 all risky 1 0.3000% 0 100% 0 w 0 w 1 w 2 (5.00%) 2 (4.00%) 2 (1.40%) 2 (2.33%) 2 (3.01%) 2

The Optimal Portfolio Solution 65.08% risk aversion 45.04% 0.1204 6 41.80% 26.22% 31.99% 45.04% 0.1204 10 15.73% 12.70% 19.19% 45.04% 0.1204 Regardless of their risk aversion, investors hold the same optimal risky This optimal risky portfolio, also known as the tangent portfolio, has the highest Sharpe ratio attainable. What separates a more risk averse investor from his more risk tolerant Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 39.32% 47.98% 4 192% 0.1204 Sharpe ratio 1 -249% 157% 19 / 52 45.04% 2 -74.61% 78.65% 95.96% 45.04% 0.1204 w ∗ w ∗ w ∗ 1 /( w ∗ w ∗ 1 + w ∗ 2 ) 0 1 2 portfolio: w ∗ 1 /( w ∗ 1 + w ∗ 2 ) is the same for all investors. counterpart is the optimal weight w 0 invested in the riskfree asset.

The Optimal Portfolio Solution The risk premium also has two elements, Jun Pan Portfolio Management Financial Markets, Day 4, Class 1 When there is only one risky asset, the optimal portfolio weight 20 / 52 elements, Now we have two risky assets, so the portfolio weight has two risk premium y ∗ = variance × risk aversion ( w 1 ) w = w 2 ( 0 . 80 % − 0 . 33 % ) ( 0 . 47 % ) risk premium = = 0 . 70 % − 0 . 33 % 0 . 37 %

The variance now has variance as well as covariance, and it is now called variance-covariance matrix. Jun Pan Portfolio Management Financial Markets, Day 4, Class 1 For example, an investor with risk aversion = 4: still applies, except that we need to use matrix notation: risk premium The optimal portfolio weight: 21 / 52 variance 2 covariance covariance ( variance 1 ) ( 5 % 2 ) 5 % × 4 % × 0 . 2 Σ = = 4 % 2 5 % × 4 % × 0 . 2 variance × risk aversion 1 w ∗ = risk aversion × Σ − 1 × risk premium ( 5 % 2 ) ( 0 . 47 % ) w ∗ = 1 5 % × 4 % × 0 . 2 − 1 4 × 4 % 2 5 % × 4 % × 0 . 2 0 . 37 %

Matrix Operations Some useful tips for matrix operation in Excel : the command for summation is still “+” the command for multiplication is “mmult” Some useful tips for matrix operation in Matlab : the command for summation is still “+” Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 22 / 52 the command for inverse, say Σ − 1 , is “minverse” the command for multiplication is still “ ∗ ” the command for inverse, say Σ − 1 , is “inv (Σ) ”

Magellan, PIMCO, and Hedge Fund Monthly Returns from 199401 to 201009 Jun Pan Portfolio Management Financial Markets, Day 4, Class 1 The optimal risky portfolio: -7.14%, 70.88%, and 36.26%. 100% 22.98% 2.23% 0.77% 22.98% 100% 1.21% 0.61% PIMCO 58.70% 13.51% 5.18% 0.60% Magellan risky asset 0 0.28% riskfree r f corr(.,H) corr(.,P) std mean 23 / 52 Hedge Fund Index ∗

On Modern Portfolio Theory The Modern Portfolio Theory is about optimal diversifjcation and optimal risk and return tradeofg. This intellectual foundation should be central to any portfolio management. The actual math, however, needs human supervision. Otherwise, it could be harmful instead of useful. Financial Markets, Day 4, Class 1 Portfolio Management Jun Pan 24 / 52