Portfolio Performance Evaluation CHAPTER 24

Introduction Complicated subject Theoretically correct measures are difficult to construct Different statistics or measures are appropriate for different types of investment decisions or portfolios Many industry and academic measures are different The nature of active management leads to measurement problems Bahattin Buyuksahin, JHU Investment

Dollar- and Time-Weighted Returns Dollar-weighted returns Internal rate of return considering the cash flow from or to investment Returns are weighted by the amount invested in each stock Time-weighted returns Not weighted by investment amount Equal weighting Bahattin Buyuksahin, JHU Investment

Text Example of Multiperiod Returns Period Action 0 Purchase 1 share at $50 1 Purchase 1 share at $53 Stock pays a dividend of $2 per share 2 Stock pays a dividend of $2 per share Stock is sold at $108 per share Bahattin Buyuksahin, JHU Investment

Dollar-Weighted Return Period Cash Flow 0 -50 share purchase 1 +2 dividend -53 share purchase 2 +4 dividend + 108 shares sold Internal Rate of Return: Bahattin Buyuksahin, JHU Investment

Time-Weighted Return Text Example Average: rG = [ (1.1) (1.0566) ]1/2 - 1 = 7.81% Bahattin Buyuksahin, JHU Investment

Adjusting Returns for Risk Benchmark portfolio Comparison with other managers of similar investment style May be misleading Bahattin Buyuksahin, JHU Investment

Figure 24.1 Universe Comparison Bahattin Buyuksahin, JHU Investment

Risk Adjusted Performance: Sharpe 1) Sharpe Index rp = Average return on the portfolio rf = Average risk free rate p = Standard deviation of portfolio return  Bahattin Buyuksahin, JHU Investment

Risk Adjusted Performance: Treynor 2) Treynor Measure rp = Average return on the portfolio rf = Average risk free rate ßp = Weighted average for portfolio Bahattin Buyuksahin, JHU Investment

Risk Adjusted Performance: Jensen 3) Jensen’s Measure  = Alpha for the portfolio p rp = Average return on the portfolio ßp = Weighted average Beta rf = Average risk free rate rm = Average return on market index portfolio Bahattin Buyuksahin, JHU Investment

Information Ratio Information Ratio = ap / s(ep) Information Ratio divides the alpha of the portfolio by the nonsystematic risk Nonsystematic risk could, in theory, be eliminated by diversification Bahattin Buyuksahin, JHU Investment

M2 Measure Developed by Modigliani and Modigliani Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolio If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market Bahattin Buyuksahin, JHU Investment

M2 Measure: Example Managed Portfolio: return = 35% standard deviation = 42% Market Portfolio: return = 28% standard deviation = 30% T-bill return = 6% Hypothetical Portfolio: 30/42 = .714 in P (1-.714) or .286 in T-bills (.714) (.35) + (.286) (.06) = 26.7% Since this return is less than the market, the managed portfolio underperformed Bahattin Buyuksahin, JHU Investment

Figure 24.2 M2 of Portfolio P Bahattin Buyuksahin, JHU Investment

Which Measure is Appropriate? It depends on investment assumptions 1) If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market 2) If many alternatives are possible, use the Jensen or the Treynor measure The Treynor measure is more complete because it adjusts for risk Bahattin Buyuksahin, JHU Investment

Table 24.1 Portfolio Performance Bahattin Buyuksahin, JHU Investment

Figure 24.3 Treynor’s Measure Bahattin Buyuksahin, JHU Investment

Table 24.2 Excess Returns for Portfolios P and Q and the Benchmark M over 12 Months Bahattin Buyuksahin, JHU Investment

Table 24.3 Performance Statistics Bahattin Buyuksahin, JHU Investment

Performance Measurement for Hedge Funds When the hedge fund is optimally combined with the baseline portfolio, the improvement in the Sharpe measure will be determined by its information ratio: Bahattin Buyuksahin, JHU Investment

Performance Measurement with Changing Portfolio Composition For actively managed portfolios, it is helpful to keep track of portfolio composition and changes in portfolio mean and risk Bahattin Buyuksahin, JHU Investment

Figure 24.4 Portfolio Returns Bahattin Buyuksahin, JHU Investment

Market Timing In its pure form, market timing involves shifting funds between a market- index portfolio and a safe asset Treynor and Mazuy: Henriksson and Merton: Bahattin Buyuksahin, JHU Investment

Figure 24. 5 Characteristic Lines: Panel A: No Market Timing Figure 24.5 Characteristic Lines: Panel A: No Market Timing. Panel B: Beta Increases with Expected Market Excess. Return Panel C: Market Timing with Only Two Values of Beta. Bahattin Buyuksahin, JHU Investment

Table 24.4 Performance of Bills, Equities and (Annual) Timers – Perfect and Imperfect Bahattin Buyuksahin, JHU Investment

Figure 24.6 Rate of Return of a Perfect Market Timer as a Function of the Rate of Return on the Market Index Bahattin Buyuksahin, JHU Investment

Figure 24.7 Scatter Diagram of Timer Performance Bahattin Buyuksahin, JHU Investment

Style Analysis Introduced by William Sharpe 1992 study of mutual fund performance 91.5% of variation in return could be explained by the funds’ allocations to bills, bonds and stocks Later studies show that 97% of the variation in return could be explained by the funds’ allocation to a broader range of asset classes Bahattin Buyuksahin, JHU Investment

Table 24.5 Style Analysis for Fidelity’s Magellan Fund Bahattin Buyuksahin, JHU Investment

Figure 24.8 Fidelity Magellan Fund Cumulative Return Difference: Fund versus Style Benchmark and Fund versus SML Benchmark Bahattin Buyuksahin, JHU Investment

Figure 24.9 Average Tracking Error for 636 Mutual Funds, 1985-1989 Bahattin Buyuksahin, JHU Investment

Morningstar Morningstar computes fund returns as well as a risk measure based primarily on fund performance in its worst years The risk-adjusted performance is ranked across funds in a style group and stars are awarded Bahattin Buyuksahin, JHU Investment

Evaluating Performance Evaluation Performance Evaluation has two problems Many observations are needed for significant results Shifting parameters when portfolios are actively managed makes accurate performance evaluation all the more elusive Bahattin Buyuksahin, JHU Investment

Figure 24.10 Rankings Based on Morningstar’s Category RARs and Excess Return Sharpe Ratios Bahattin Buyuksahin, JHU Investment

Performance Attribution Decomposing overall performance into components Components are related to specific elements of performance Example components Broad Allocation Industry Security Choice Up and Down Markets Bahattin Buyuksahin, JHU Investment

Attributing Performance to Components Set up a ‘Benchmark’ or ‘Bogey’ portfolio Use indexes for each component Use target weight structure Bahattin Buyuksahin, JHU Investment

Attributing Performance to Components Continued Calculate the return on the ‘Bogey’ and on the managed portfolio Explain the difference in return based on component weights or selection Summarize the performance differences into appropriate categories Bahattin Buyuksahin, JHU Investment

Formula for Attribution Where B is the bogey portfolio and p is the managed portfolio Bahattin Buyuksahin, JHU Investment

Figure 24.11 Performance Attribution of ith Asset Class Bahattin Buyuksahin, JHU Investment

Table 24.6 Performance of the Managed Portfolio Bahattin Buyuksahin, JHU Investment

Table 24.7 Performance Attribution Bahattin Buyuksahin, JHU Investment

Table 24.8 Sector Selection within the Equity Market Bahattin Buyuksahin, JHU Investment

Table 24.9 Portfolio Attribution: Summary Bahattin Buyuksahin, JHU Investment

International Diversification CHAPTER 25

Background Global market US market is 39.2% of all markets in 2005 US market share is down from 47% in 2000 Improved access & technology New instruments Emphasis for our investigation Risk assessment Diversification Bahattin Buyuksahin, JHU Investment 46

Table 25.1 Market Capitalization of Stock Exchanges in Developed Countries Bahattin Buyuksahin, JHU Investment

Table 25.2 Market Capitalization of Stock Exchanges in Emerging Markets Bahattin Buyuksahin, JHU Investment

Figure 25.1 Per Capita GDP and Market Capitalization as Percentage of GDP (log scale) Bahattin Buyuksahin, JHU Investment

Issues What are the risks involved in investment in foreign securities? How do you measure benchmark returns on foreign investments? Are there benefits to diversification in foreign securities? Bahattin Buyuksahin, JHU Investment

Foreign Exchange Risk Foreign Exchange Risk Variation in return related to changes in the relative value of the domestic and foreign currency Total return = investment return & return on foreign exchange It’s not possible to completely hedge a foreign investment Bahattin Buyuksahin, JHU Investment 51

Returns with Foreign Exchange Return in US is a function of two factors: 1. Return in the foreign market 2. Return on the foreign exchange Bahattin Buyuksahin, JHU Investment 52

Figure 25. 2 Stock Market Returns in U. S Figure 25.2 Stock Market Returns in U.S. Dollars and Local Currencies for 2005 Bahattin Buyuksahin, JHU Investment

Table 25. 3 Rates of Change in the U. S Table 25.3 Rates of Change in the U.S. Dollar Against Major World Currencies, 2001 – 2005 (Annualized from monthly data) Bahattin Buyuksahin, JHU Investment

Hedging Exchange Rate Risk Futures or forward markets are used to eliminate the risk of holding another asset The U.S. investor can lock in a riskless dollar- denominated return either by investing in UK bills and hedging exchange rate risk or by investing riskless U.S. assets Bahattin Buyuksahin, JHU Investment

Country Specific Risk Political Risk Services Group Ratings Rank countries with respect to political risk, financial risk and economic risk Assign composite rating from very high risk to very low risk based on the above elements of risk Bahattin Buyuksahin, JHU Investment 56

Table 25.4 Composite Risk Ratings for October 2004 and November 2003 Bahattin Buyuksahin, JHU Investment

Table 25.5 The Three Ratings that Comprise ICRG’s Composite Risk Rating Bahattin Buyuksahin, JHU Investment

Table 25.6 Current Risk Ratings and Composite Risk Forecasts Bahattin Buyuksahin, JHU Investment

Table 25.7 Composite and Political Risk Forecasts Bahattin Buyuksahin, JHU Investment

Table 25.8 Political Risk Points by Component, October 2004 Bahattin Buyuksahin, JHU Investment

Diversification Benefits Evidence shows international diversification is beneficial It’s possible to expand the efficient frontier above domestic only frontier It’s possible to reduce the systematic risk level below the domestic only level Bahattin Buyuksahin, JHU Investment

Table 25.9 Risk and Return Across the Globe, 2001 – 2005 (Developed Countries and Emerging Markets) Bahattin Buyuksahin, JHU Investment

Figure 25.3 Annualized Standard Deviation of Investments Across the Globe ($ returns, 2001 – 2005) Bahattin Buyuksahin, JHU Investment

Figure 25.4 Beta on U.S. Stocks Across the Globe, 2001–2005 Bahattin Buyuksahin, JHU Investment

Figure 25.5 Annualized Average $ Return of Investments Across the Globe, 2001 – 2005 Bahattin Buyuksahin, JHU Investment

Figure 25.6 Standard Deviation of Investments Across the Globe in U.S. Dollars versus Local Currency, 2001 – 2005 Bahattin Buyuksahin, JHU Investment

Table 25.10 Correlation for Asset Returns: Unhedged and Hedged Currencies Bahattin Buyuksahin, JHU Investment

Table 25. 11 Correlation of U. S Table 25.11 Correlation of U.S. Equity Returns with Country Equity Returns Bahattin Buyuksahin, JHU Investment

Figure 25.7 International Diversification Bahattin Buyuksahin, JHU Investment

Figure 25.8 Ex Post Efficient Frontier of Country Portfolios, 2001 – 2005 Bahattin Buyuksahin, JHU Investment

Figure 25.9 Efficient Frontier of Country Portfolios (world expected excess return = .6% per month) Bahattin Buyuksahin, JHU Investment

Figure 25.10 Regional Indexes around the Crash, October 14–October 26, 1987 Bahattin Buyuksahin, JHU Investment

Figure 25.11 Efficient Diversification by Various Methods Bahattin Buyuksahin, JHU Investment

Figure 25.12 Diversification by Market Capitalization: National Markets versus Regional Funds Bahattin Buyuksahin, JHU Investment

Figure 25.13 Diversification Benefits over Time Bahattin Buyuksahin, JHU Investment

Table 25.12 Weighting Schemes for EAFE Countries Bahattin Buyuksahin, JHU Investment

Performance Attribution with International Extension to consider additional factors Currency selection Country selection Stock selection Cash and bond selection Bahattin Buyuksahin, JHU Investment

Table 25.13 Example of Performance Attribution: International Bahattin Buyuksahin, JHU Investment

Hedge Funds CHAPTER 26

Hedge Funds Characteristics Investment pooling Transparency Limited liability partnerships Provide minimal information Investors No more than 100 “sophisticated” investors Investment strategies Wide range of investments Bahattin Buyuksahin, JHU Investment

Hedge Funds Characteristics Continued Liquidity Lock-up periods Compensation structure Charge a management fee plus a substantial incentive fee Bahattin Buyuksahin, JHU Investment

Hedge Fund Strategies Directional Bets that one sector or another will outperform other sectors Non directional Exploit temporary misalignments in security valuations Buys one type of security and sells another Strives to be market neutral Bahattin Buyuksahin, JHU Investment

Table 26.1 Hedge Fund Styles Bahattin Buyuksahin, JHU Investment

Statistical Arbitrage Uses quantitative systems that seek out many temporary misalignments in prices Involves trading in hundreds of securities a day with short holding periods Pairs trading Pair up similar companies whose returns are highly correlated but one is priced more aggressively Create a market-neutral position Data mining Bahattin Buyuksahin, JHU Investment

Alpha Transfer Separate asset allocation from security selection Invest where you find alpha Hedge the systematic risk to isolate its alpha Establish exposure to desired market sectors by using passive indexes Bahattin Buyuksahin, JHU Investment

Pure Play Example From the Text Manage a $1.5 million portfolio Believe alpha is >0 and that the market is about to fall Capture the alpha of 2% per month β = 1.20 S&P 500 Index is S0 = 1,440 α = .02 rf = .01 Hedge by selling S&P 500 futures contracts Bahattin Buyuksahin, JHU Investment

Pure Play Example Continued The dollar value of your portfolio after 1 month: The dollar proceeds from your futures position: Bahattin Buyuksahin, JHU Investment

Figure 26. 1 A Pure Play. Panel A, Unhedged Position Figure 26.1 A Pure Play. Panel A, Unhedged Position. Panel B, Hedged Position Bahattin Buyuksahin, JHU Investment

Style Analysis Hasanhodzic and Lo factors: Equity market conditions Foreign exchange Interest rates Credit conditions Commodity markets Volatility Bahattin Buyuksahin, JHU Investment

Table 26.2 Style Analysis for a Sample of Hedge Funds Bahattin Buyuksahin, JHU Investment

Liability and Hedge Fund Performance Hedge funds tend to hold more illiquid assets than other institutional investors Aragon Typical alpha may be interpreted as an equilibrium liquidity premium than a sign of stock-picking ability Santa Effect Higher returns reported in December Stronger for lower-liquidity funds Bahattin Buyuksahin, JHU Investment

Table 26.3 Performance Measures for Hedge Funds Bahattin Buyuksahin, JHU Investment

Figure 26.2 Hedge Funds with Higher Serial Correlation in Returns, an Indicator of Illiquid Portfolio Holdings, Exhibit Higher Sharpe Ratios Bahattin Buyuksahin, JHU Investment

Hedge Fund Performance and Survivorship Bias Backfill bias Hedge funds report returns to database publishers only if they choose to Survivorship bias Unsuccessful funds that cease operation stop reporting returns and leave a database Only successful funds remain Bahattin Buyuksahin, JHU Investment

Hedge Fund Performance and Changing Factor Loadings Hedge funds are designed to be opportunistic and have considerable flexibility to change profiles If risk is not constant Alphas will be biased if a standard, linear index model is used Bahattin Buyuksahin, JHU Investment

Figure 26.3 Characteristic Line of a Perfect Market Timer Bahattin Buyuksahin, JHU Investment

Figure 26.4 Characteristic Lines of Stock Portfolio with Written Options Bahattin Buyuksahin, JHU Investment

Table 26.4 Index Model Results for Hedge Funds, Allowing for Different Up- and Down-Market Betas Bahattin Buyuksahin, JHU Investment

Black Swans and Hedge Fund Performance Nassim Taleb: Many hedge funds rack up fame through strategies that make money most of the time, but expose investors to rare but extreme losses Examples: The October 1987 crash Long Term Capital Management Bahattin Buyuksahin, JHU Investment

Fee Structure in Hedge Funds Typical hedge fund fee structure Management fee of 1% to 2% of assets Incentive fee equal to 20% of investment profits beyond a stipulated benchmark performance Effectively call options on the portfolio with a strike price equal to current portfolio value High water mark The fee structure can give incentives to shut down a poorly performing fund Bahattin Buyuksahin, JHU Investment

Figure 26.5 Incentive Fees as a Call Option Bahattin Buyuksahin, JHU Investment

Funds of Funds Invest in several other hedge funds Optionality can have a big impact on expected fees Fund of funds pays an incentive fee to each underlying fund that outperforms its benchmark even if the aggregate performance is poor Diversification can actually hurt the investor in this case Bahattin Buyuksahin, JHU Investment

Funds of Funds Continued Spread risk across several different funds Investors need to be aware that these funds of funds operate with considerable leverage If the various hedge funds in which these funds of funds invest have similar investment styles, diversification may illusory Bahattin Buyuksahin, JHU Investment

Example 26.6 Incentive Fees in Funds of Funds A fund of funds is established with $1 million invested in each of three hedge funds Hurdle rate for the incentive fee is a zero return Each fund charges an incentive fee of 20% The aggregate portfolio of the fund of funds is -5% Still pays incentive fees of $.12 for every $3 invested Fund 1 Fund 2 Fund 3 Fund of Funds Start of year (millions) $1.00 $2.00 $3.00 End of year (millions) $1.20 $1.40 $0.25 $2.85 Gross rate of return 20% 40% -75% -5% Incentive fee (millions) $0.04 $0.08 $0.00 $0.12 End of year, net of fee $1.16 $1.32 $.25 $2.73 Net rate of return 16% 32% -9% Bahattin Buyuksahin, JHU Investment

The Theory of Active Portfolio Management CHAPTER 27

Overview Treynor-Black model Optimization using analysts’ forecasts of superior performance Adjusting model for tracking error Adjusting model for analyst forecast error Black-Litterman model Bahattin Buyuksahin, JHU Investment

Table 27.1 Construction and Properties of the Optimal Risky Portfolio Bahattin Buyuksahin, JHU Investment

Table 27.2 Stock Prices and Analysts’ Target Prices for June 1, 2006 Bahattin Buyuksahin, JHU Investment

Figure 27.1 Rates of Return on the S&P 500 (GSPC) and the Six Stocks, June 2005 – May 2006 Bahattin Buyuksahin, JHU Investment

Table 27.3 The Optimal Risky Portfolio with the Analysts’ New Forecasts Bahattin Buyuksahin, JHU Investment

Table 27.4 The Optimal Risky Portfolio with Constraint on the Active Portfolio (WA < 1) Bahattin Buyuksahin, JHU Investment

Figure 27.2 Reduced Efficiency when Benchmark is Lowered Bahattin Buyuksahin, JHU Investment

Table 27.5 The Optimal Risky Portfolio with the Analysts’ New Forecasts (benchmark risk constrained to 3.85%) Bahattin Buyuksahin, JHU Investment

Adjusting Forecasts for the Precision of Alpha How accurate is your forecast How should you adjust your position to take account of forecast imprecision Must quantify the uncertainty by examining the forecasting record of previous forecasts by same forecaster The adjusted alpha: Bahattin Buyuksahin, JHU Investment

Figure 27.3 Histogram of the Alpha Forecast Bahattin Buyuksahin, JHU Investment

Figure 27.4 Organizational Chart for Portfolio Management Bahattin Buyuksahin, JHU Investment

Steps in the Black-Litterman Model Step 1: Estimate the covariance matrix from historical data Step 2: Determine a baseline forecast Step 3: Integrating the manager’s private views Step 4: Developing revised (posterior) expectations Step 5: Apply portfolio optimization Bahattin Buyuksahin, JHU Investment

Figure 27.5 Sensitivity of Black-Litterman Portfolio Performance to Confidence Level (view is correct) Bahattin Buyuksahin, JHU Investment

Figure 27.6 Sensitivity of Black-Litterman Portfolio Performance to Confidence Level (view is false) Bahattin Buyuksahin, JHU Investment

The BL Model as Icing on the TB Cake Suppose that you have two portfolios—one for the US and one for Europe The model would be run as two separate divisions Each division would compile values of alpha relative to their own passive portfolio Relative performance of the two markets can be expected to add information to the independent macro forecasts for the two economies Portfolios need to be optimized separately Bahattin Buyuksahin, JHU Investment

Value of Active Management Model for estimation of potential fees Kane, Marcus, and Trippi derive an annuitized value of portfolio performance measured as a percent of funds under management The percentage fee that investors would be willing to pay for active services can be related to the difference between the square of the portfolio Sharpe ratio and that of the passive portfolio Source of the power of the active portfolio is the additive value of the squared information ratios Bahattin Buyuksahin, JHU Investment

Table 27.6 M-Square for the Portfolio, Actual Forecasts Bahattin Buyuksahin, JHU Investment

Table 27.7 M-Square of Simulated Portfolios Bahattin Buyuksahin, JHU Investment

Concluding Remarks The gap between theory and practice has been narrowing in recent years The CFA is expanding knowledge base in the industry Specific lack of application of the Treynor-Black model may be related to lack of application of adjusting for analysts’ errors Bahattin Buyuksahin, JHU Investment