L20 Active Portfolio Management

15.433 INVESTMENTS Class 20: Active Portfolio Management Spring 2003 Financial instruments are increasing in number and complexity Supranationals Interest rate-options Cross-currency hedges Currency- Currency- forwards options AgenciesAgencies Proxy hedges Complex domestic markets Government FuturesFutures Index-linked bonds Semigovernments SwapsSwaps Volatility options AgenciesAgencies Inflation protected SupranationalsSupranationals government bonds Swaptions CDO / MBA Exotic currency options Key question for every investor What is the goal for the total portfolio? What is the time frame for achieving that goal? What is the tolerance for loss/uncertainty within a shorter term (one-, three-, six-month) period? Which kinds of risk are acceptable/unacceptable? What are you willing to pay for active risk management? (e.g. cur - rency hedges) How do you monitor/evaluate your risk management? The risk-versus-return compass Increasing compensated risks can increase returns Two major types of compensated risk: • Credit • Market Are these areas of ”skill” ? Optimize the risk exposure Insufficient evidence of ”skill” ? Ignore, hedge or transfer the risk? Same Risk More Return Less Risk Starting Portfolio Starting Portfolio More Risk Same Return Same Return Same Risk Less Return Higher Moments of Asset Asset −→ Return −→ Risk ∂(asset) ∂∆ = return change in value of asset ∂(return) = risk speed of change ∂∆ ∂(risk) = higher moments of risk profile of speed ∂∆ Active vs. Passive management Active management means allocation of resources based on an active strategy. Usually active management is performed against a benchmark, requiring intended over-/ underweights of positions. Passive management means following an index, benchmark or another portfolio using quantitative techniques, such as principal component analysis to replicate an index. The discussion of active vs passive management is linked to the effi- cient market discussion: Can information add value (performance). Strategic Asset Allocation Tactical Asset Allocation Stock Picking To p- Do wn Bo tto m -U p Figure 3: Bottom-up vs. top down approach From Where does Superior Performance Come? From Where does Superior Performance Come? Superior performance arises from active investment decisions which differentiate the portfolio from a ”passive” benchmark These decisions include: • Market Timing: Altering market risk exposure through time to make advantage of market fluctuations; • Sectoral emphasis: Weighting the portfolio towards (or away from) company attributes, such as size, leverage, book/price, and yield, and towards (or away from) industries; • Stock selection: Marking bets in the portfolio based on informa- tion idiosyncractic to individual securities; • Trading: large funds can earn incremental reward by accommodat- ing hurried buyers and sellers. Some Definitions Active management: The pursuit of transactions with the objective of profiting from competitive information - that is, information that would lose its value if it were in the hands of all market participants Active man- agement is characterized by a process of continued research to generate superior judgment, which is then reflected in the portfolio by transac- tions that are held in order to profit from the judgment and that are liquidated when the profit has been earned. Alpha: The ”risk adjusted expected return” or the return in excess of what would be expected from a diversified portfolio with the same sys- tematic risk When applied to stocks, alpha is essentially synonymous with misvaluation: a stock with a positive alpha is viewed as under- valued relative to other stocks with the same systematic risk, and a stock with a negative alpha is viewed as overvalued relative to other stocks with the same systematic risk When applied to portfolios, alpha is a description of extraordinary reward obtainable through the portfolio strategy. Here it is synonymous with good active management: a bet- ter active manager will have a more positive alpha at a given level of risk. Alpha, historical: The difference between the historical performance and what would have been earned with a diversified market portfolio at the same level of systematic risk over that period. Under the simplest proce- dures, historical alpha is estimated as the constant term in a time series regression of the asset or portfolio return upon the market return. Alpha, judgmental: The final output of a research process, embody- ing in a single quantitative measure the degree of under or overvaluation of the stocks Judgmental alpha is a product of investment research and unique to the individual or organization that produces it is derived from a ”forecast” of extraordinary return, but it has been adjusted to be the expected value of subsequent extraordinary return. For example, among those stocks that are assigned judgmental alphas of 2 percent, the aver- age performance (when compared to other stocks of the same systematic risk with alphas of zero) should be 2 percent per annum. Thus, average experienced performance for any category of judgmental alpha should equal the alpha itself. A judgmental alpha is a prediction, not retro- spective experience. Alpha, required: The risk adjusted expected return required to cause the portfolio holding to be optimal, in view of the risk/reward tradeoff. The required alpha is found by solving for the contribution of the hold- ing to portfolio risk and by applying a risk/reward tradeoff to find the corresponding alpha. It can be viewed as a translation of portfolio risk exposure into the judgment which warrants that exposure. CAPM Ex pe ct ed R et ur n Beta (β) Se cu rit y M ark et Lin e M (rf) β = 1 (rM) Expected Risk Premium defensive aggressive Risk free Investment Investment in Market Figure: CAPM and market-aggressivity E (ri) − rf βi = (1) E (rM ) − rf cov (ri, rM ) βi = σ2 (2) M APT APT says: • Expected excess return for any asset is a weighted combination of the asset’s exposure to factors. APT does not say: • What the factors are or what the weights are. So what? • CAPM forecasts can be used for performance measurement, i.e. beat the index; • APT forecasts are difficult to use for performance - remember they are arbitrary; • A good APT forecast can help you to outperform the index; • APT is an active management tool based on a multifactor model. Factor Models R2 = 1 − var (εi) (3) var (ri) ri = [bi,1F1 + bi,2F2 + · · ·+ bi,nFn] (4) A factor models tries to explain the variation of return, which is a trans- formation of the original level: asset behavior. Some techniques help to understand what moves the assets and thus determines return and risk. The principal component analysis is fre- quently used, but . . . first hand interpretation is maybe not intuitive . ”Shall I go long principal component 2 and short principal component 4 ?” Le Penseur, Rodin 1880 The Treynor-Black Model Mix Security Analysis with Portfolio Theory Suppose that you find several securities appear to be mispriced relative to the pricing model of your choice, say the CAPM. According to the CAPM, the expected return of any security with βk is: CAPM µ = rf + βk · (E (rM ) − rf) (5) k Let A be subset with ”mis-priced” securities. For any security k ∈ A, you find that CAPM rk = αk + µk + εk (6) where αk is the perceived abnormal return. You would like to exploit the ”mis-pricing” in the subset A. For this, your form a portfolio A, consisting of the ”mis-priced” securities. At the same time, you believe that the rest of the universe is fairly priced. The rest of the portfolio allocation problem then becomes a standard one: • The objective is that of a mean-variance investor. • The choice of assets: 1. The market portfolio with µM and σM 2. The portfolio of ”mis-priced” securities A, 3. with µA and σA 4. The riskfree asset. • The solution: same as the one we considered in Class 5. The Black-Litterman Model Mix Beliefs with Portfolio Theory The Black-Litterman asset allocation model, developed when both au- thors were working for Goldman Sachs, is a significant modification of the traditional mean-variance approach. In the mean-variance approach of Markowitz, the user inputs a complete set of expected returns and the variance-covariance matrix, and the portfolio optimizer generates the op- timal portfolio weights. Due to the complex mapping between expected returns and portfolio weights, users of the standard portfolio optimizers often find that their specification of expected returns produces output portfolio weights which may not make sense. These unreasonable results stem from two well recognized problems: 1. Expected returns are very difficult to estimate. Investors typically have knowledgeable views about absolute or relative returns in only a few markets. A standard optimization model, however, requires them to provide expected returns for all assets. 2. The optimal portfolio weights of standard asset allocation models are extremely sensitive to the return assumptions used. These two problem compound each other; the standard model has no way to distinguish strongly held views from auxiliary assumptions, and the optimal portfolio it generates, given its sensitivity to the expected returns, often appears to bear little or no relation to the views the in- vestor wishes to express. In practice, therefore, despite the obvious attractions of a quantitative approach, few global investment managers regularly allow quantitative models to play a major role in their asset allocation decision. In the Black-Litterman model, the user inputs any number of views or state- ments about the expected returns of arbitrary portfolios, and the model combines the views with equilibrium, producing both the set of expected returns of assets as well as the optimal portfolio weights. Since publi- cation of 1990, the Black-Litterman asset allocation model has gained wide application in many financial institutions. How relevant are factors in relation to different styles? 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 PC 9 PC 10 PC 1 PC 2 PC 3 PC 4 PC 5 PC 6 PC 7 PC 9 PC 10 Factors for ”Value” portfolio Factors for ”Growth” portfolio Depending on the nature of the investments, the influencing factors are different. Thus, the principal components, reflecting the ”explanatory power” of existing, but ”unknown” factors are different in structure and dimension. What makes a ”good” factor? • Interpretable: It is based on fundamental and market-related char- acteristics commonly used in security analysis • Incisive: It divides the market into well defined slices • Interesting: It contributes significantly to risk, or it has persistent or cyclical positive or negative exceptional return Why Factors? • Change in behavior (company restructuring, new business strategy etc), • reflected in sensitivities to factors; Screening of universe for ”ade- quate” investments, depending on investment objective; • Handling of information-overflow Some examples of Style-definitions: • Large Cap Value: Stocks in Standard & Poor’s 500 index with high book-to-price ratios • Large Cap Growth: Stocks in Standard & Poor’s 500 index with low book-to-price ratios • Small Cap Stocks: Stocks in the bottom 20 • Each styles reacts different and thus fits different clients in different ways Factor Definitions: Size: Captures differences in stock returns due to differences in the mar- ket capitalization of companies This index continues to be a significant determinant of performance as well as risk. Success: Identifies recently successful stocks using price behavior in the market as measured by relative strength. The relative strength of a stock is significant in explaining its volatility. Value: Captures the extent to which a stock is priced inexpensively in the market. The descriptors are as follows: • Forecast Earnings to Price; • Actual Earnings to Price; • Actual Earnings to Price; • Yield. Variability in Markets (VIM): Predicts a stock’s volatility, net of the market, based on its historical behavior. Unlike beta, this index mea- sures the stock’s overall volatility. Growth: Uses historical growth and profitability measures to predict future earnings growth. The descriptors are as follows: • Dividend payout ratio over five years Computed using the last five years of data on dividends and earnings; • Variability in capital structure; • Growth rate in total assets; • Earnings growth rate over last five years; • Analyst-predicted earnings growth; • Recent earnings change Measure of recent earnings growth. Return Decomposition Total Return ActiveNormal Risk-FreeTotal Excess Active Specific Active Systematic Figure: Return decomposition Risk Decomposition Common Risk 21 x 21 = 441 Specific Risk 4.5 x 4.5 = 20.25 Total Risk 21.48 x 21.48 = 461.25 Figure: Risk decomposition, � � � � � Return and Risk, A Two Factor Linear Model Return: rp = ap + bp,1F1 + bp,2F2 + εp rBM = aBM + bBM,1F1 + bBM,2F2 + εBM (7) Excess Return: rp − rBM = ap + (bp,1 − bBM,1 )F1 + (bp,2 − bBM,2) F2 + (ap + εp − aBM − εBM ) (8) Variance of Excess Return : 2 2 var (rp − rBM ) = (bp,1 − bBM,1) var (F1) + (bp,2 − bBM,2) (F2) + 2 · (bp,1 − bBM,1) (bp,2 − bBM,2) · cov (F1, F2) + var (εp) + var (εBM ) − 2 · cov (εp, εBM ) (9) Tracking Error: � 2 2 � (bp,1 − bBM,1) var (F1) + (bp,2 − bBM,2) (F2) TE = varp − rBM = � +2· (bp,1 − bBM,1) (bp,2 − bBM,2) · cov (F1, F2) (10) +var(εp) + var (εBM ) − 2 · cov (εp, εBM ) 23 MIT Sloan 15.433 Tracking Error The tracking error is defined as: ”the standard deviation of active re- turn”. σA = std [rAP ] = σ [rP ] − σ [rBM ] = σAP = σP − σBM (11) The tracking error measures the deviation from the benchmark, as the rp is the sum of the weighted returns of all positions in the portfolio and rBM is the sum of the weighted returns of all positions in the benchmarks. Portfolio and benchmark do not always contain the same positions! Tracking error is called as well active risk. Information Ratio Information Ratio: A measure of a portfolio manager’s ability to deliver, relating the relative return to the benchmark and the relative risk to the benchmark: • Expected Active Return (alpha) • Active Risk expected active return α IR = = (12) active risk T E Implied alpha: Alpha backed-out through reverse engineering; how much has my expected return to be to justify all other parameters ceteris paribus Forecasts Some examples: • MCAR: How much does active risk increase if I increase the holding x by 1 % and reduce cash by 1 % • MCTCFR: How much does common factor risk increase if I increase the holding x by 1 % and reduce cash by 1 % • MCASR: How much does specific active risk increase if I increase the holding x by 1 % and reduce cash by 1 % Performance Attribution The identification of individual return components can be performed quite easily, subject to the history of the restructuring of the portfolio. The straight forward approach is based on the definition of a passive benchmark portfolio, which reflects the long-term investment strategy. In the context of the investment strategy (or the strategic asset alloca- tion) the investment management decides which asset categories (equi- ties, fixed income, currencies, etc.) are over-/underweighted relative to the benchmark (strategy). The weights of specific asset categories - as determined in the investment strategy - are called normal weights. For each asset category of the portfolio exists a corresponding asset cat- egory of the benchmark (index), relative to which the performance is calculated. The return of these indices are called normal returns. It is obvious, that the the normal return is a return of a passive investment in the corresponding asset category of the benchmark. For equities, fixed income and for currencies exist different indices, re- flecting different needs. The normal weight of the asset category i (ws,i) multiplied with the nor- mal return (rs,i) is the return of this intended asset category. Summed up over all returns from the different asset categories, the portfolio has the following strategy/-benchmark return: �N rstrategy = i=1 ws,i · rs,i Against this benchmark-portfolio we want to know the realized return of the actively managed portfolio. We have a positive excess-return, if the effectively realized portfolio return (rportf olio) exceeds the strategy return (rstratey): rexcess return = rstrategy − rportf olio The current portfolio return (rportf olio) is calculated from the effective breakdown of the portfolio in the different asset categories (wp,i) as well as the effectively realized returns (rs,i) of the individual asset categories: �N rportf olio = i=1 wp,i · rp,i The difference between the strategy return and the realized portfolio return results from the fact, that the portfolio manager restructures the portfolio through market timing strategies based on the on the assump- tion of predicting the direction of the performance. Overperformance by timing the market can be achieved by adjusting the overall market exposure of the portfolio. Various techniques exist to time the market: • tactical over- and underweights of categories and thus deviates from the normal weights thourghchanges in the asset class mix (especially stock and cash positions), also called rotation (sector rotation, asset class rotation) • timing within an asset class: changing the security mix by shifting the proportions of conservative (low beta) and dynamic (high beta) securities. • derivatives instruments: especially index futures and the use of op- tions. Security selection is the identification of over/-under priced securities. So a superior valuation process is needed to compare the true value for a security with the current market value. Overall, the return of a portfolio can be decomposed in four return com- ponents, which summed up again result in (rportf olio): �N • rstrategy = i=1 ws,i · rs,i �N • rtiming = i=1 rs,i · (wp,i − ws,i) �N • rselectivity = i=1 ws,i · (rp,i − rs,i) �N • rcumulative ef f ect = i=1 (wp,i − ws,i) · (rp,i − rs,i) Figure 1 highlights the decomposition of the portfolio return in the in- dividual components and their relationship to a active respectively pas- sive portfolio management. Quadrant (1) is put together from passive selectivity and passive timing. It represents the long-term investment strategy and serves as the benchmark return for the observation period in examination. If the portfolio management performs a passive market timing, we receive the return in quadrant (2). It represents the return from timing and strategy. We understand timing as the deviation in the weight of the individual asset category from the normal weight. Within the individual asset categories we invest in a passive index portfolio. Through subtraction of the strategy return from quadrant (1) we re- ceive the net result from timing. Quadrant 3 reflects the returns from selectivity and strategy. Selectivity is the active choice of individual securities within an asset strategy. The normal weights are kept equal. The return from selectivity is received through subtraction of the strategy re