Portfolio Management

1. Portfolio Management Grenoble Ecole de Management MSc Finance 2011

2. Learning Objectives Mastering the principles of the portfolio management process: • Monitoring and rebalancing • Re-sampling: active portfolio management

3. Constant monitoring • capital markets conditions change: if a client ‘s return requirement is 8% but the strategic asset allocation promises to return on average 6.5% what change s the manager should operate ? • fluctuations in the market values of assets create differences between a portfolio’s current and strategic asset allocation. These differences may be trivial on a daily basis; over longer periods of time, they can result in a significant divergence in terms of returns.

4. Monitoring • Items to be monitored: • Investors circumstances, including constraints • Market and economic changes • The portfolio itself (balance of risk)

5. Monitoring: investors circumstances • liquidity requirements • Time horizons • Tax circumstances • Changes in laws and regulations • Unique circumstances

6. Monitoring: market and economic changes • Monitoring the business cycle. The economy moves through phases of expansion and contraction. Central bank policies, yield curve movements and inflation are key factors. • Changes in asset risk attributes: an asset allocation that once promised to satisfy an investor’s investment objectives may no longer do so.

7. Monitoring the portfolio Adjusting the actual portfolio to the current strategic asset allocation because of price changes in portfolio holdings: this is rebalancing. A customer holds a portfolio with the following strategic allocation 50% in equities and 50% in bonds. The initial value of the fund is 100. Between t and t+1 the performance of the equity market is 20% while the performance of the bonds market is 2%. The value of the fund in t+1 is 111 The share of equities in this portfolio is now 54,05% The share of bonds in this portfolio is now 45,95% As a result the portfolio is no longer in line with the strategic allocation.

8. Rebalancing the portfolio • Rebalancing benefits the investor by reducing the present value of expected losses from not tracking the optimum. • It stops the capitalization process. Hence reducing the exposition to sudden reversal. • It controls drift in the overall level of risk, also the type risk of exposure drift. • Finally not rebalancing may mean holding assets that have become overpriced, offering inferior future rewards.

9. Rebalancing the portfolio • It stops the capitalization process. Hence reducing the exposition to sudden reversal. • Example: starting with the proceeding portfolio weights 45,95% in bonds and 54,05% in equities. A sudden reversal of -20% in the performance of the equity market from t+1 to t+2 would cost (for a flat performance in the bonds market): • roughly 12 to the portfolio, bringing its value to 99 and the share of equities to 48,48%. • only 11 for the rebalanced portfolio, bringing its value back to 100 but with new weights of 44,5% in stocks and 55,5% in bonds. • The cost of not rebalancing is 1 or 0,9%. This is the cost of capitalizing.

10. Rebalancing the portfolio • But rebalancing has also costs: • transaction costs (bid ask spread): their cumulative erosion of value can significantly deteriorate portfolio performances. • rebalancing means selling appreciated asset classes and buy depreciated ones. In most jurisdictions the sale of appreciated assets triggers a tax liability for taxable investors.

11. Rebalancing discipline • Calendar rebalancing • Calendar rebalancing involves rebalancing to target weights on a periodic basis, monthly, quarterly. • Calendar rebalancing can suffice in ensuring that the actual portfolio does not drift away from target for long period of time. • The significance of the rebalancing movement is key to limit costs.

12. Rebalancing • % rebalancing. • Setting rebalancing thresholds or trigger points stated as % of the portfolio’s value. Tolerance bands are more appropriate than precise thresholds. • The portfolio is rebalanced when an asset class’s weight first passes through one of its rebalancing thresholds.

13. Rebalancing • How to set the corridor ? • Ad hoc decision or linked to correlation. • higher correlation should lead to the acceptance of wider bands because deviation should not cost much in terms of returns. • higher volatility should lead to narrower corridor. Because the chance of a large movements while being away from the target is higher.

14. Rebalancing • Combination of calendar and % rebalancing is also adequate. • Tactical rebalancing might be introduced. Rebalancing might be less frequent when markets seem trending. • Also rebalancing to certain extent (partial rebalancing) might limit the cost of the operation.

15. Re-sampling • permanent, continuous revision of the forecasts then weights • the goal is to capture the largest alpha possible

16. The lure of active management • How can a theory of active portfolio management be reconciled with the notion that markets are in equilibrium? • Competition for realizing abnormal return by adding mispriced securities to portfolio ensures that prices are near fair values. • the market seems to be nearly semi-efficient. But the market is often shocked by news.

17. The lure of active management • If the market is efficient, no one has the incentive to hold a portfolio different from the market portfolio, this is passive management. • Otherwise there are incentives to differ from the market portfolio as long as the cost of research is below abnormal returns. • That’s why the strong form of efficiency cannot exists.

18. Objectives of active portfolios • The quality of active management may be measured by performance appraisal: • Jensen’s alpha • Treynor ratio • Sharpe ratio

19. Risk adjusted performance appraisal measures • The mean-variance portfolio theory implies that the objective of professional portfolio managers is to maximize the (ex ante) sharpe measure which entails maximizing the slope of the CAL. • A good manager is one whose CAL is steeper than the CAL representing the passive strategy. • Clients can observe rates of return and compute the realized sharpe measure (the ex post cal) to evaluate the relative performance of their manager.

20. Market timing The market timing is the first source of active management. Buy and hold strategy and perfect foresight on TOTAL share

21. Security selection • Security analysis is the other form of active portfolio management • Mispriced securities offer positive alpha and arbitrage situations • Balance between aggressive exploitation of perceived security mispricing and diversification: a few stocks should not dominate the portfolio.

22. Treynor-Black framework • The essence of the model is this: • Security analysts in an active investment management organization can analyze in depth only a limited number of stocks out of the entire universe of securities. The securities not analyzed are assumed to be fairly priced. • For the purpose of efficient diversification, the market index portfolio is the baseline portfolio, which the model treats as the passive portfolio. • The macro forecasting unit of the investment management firm provides forecasts of the expected return and variance of the passive (market-index) portfolio. • The objective of security analysis is to form an active portfolio of a necessarily limited number of securities. Perceived mispricing of the analyzed securities is what guides the composition of this active portfolio.

23. Treynor-Black framework Analysts follow several steps to make up the active portfolio and evaluate its expected performance: Estimate the beta of each analyzed security and its residual risk. From the beta and macro forecast, determine the required rate of return of the security (SML). Given the degree of mispricing of each security, determine its expected return and expected abnormal return (alpha) The cost of less than full diversification comes from the nonsystematic risk of the mispriced stock, the variance of the stock’s residual, sigma², which offsets the benefit (alpha) of specializing in an underpriced security. Use the estimates for the values of alpha, beta to determine the optimal weight of each security in the active portfolio Compute the alpha beta of the active portfolio from the weights of the securities in the portfolio.

24. Portfolio construction: Treynor-Black First step is evaluate the expected return of securities in the passive portfolio using the SML The objective is to form an active portfolio of positions Where αkrepresents the extra expected return (called the abnormal return) attributable to any perceived mispricing of the security. Thus for each security analyzed the research team estimates the parameter alpha beta and sigma

25. Portfolio construction: TB Given their perceived superior analysis, they will view the market –index portfolio as inefficient: the active portfolio A, constructed from mispriced securities, must lie, by design above the SML.

26. Portfolio construction: TB • Because the active portfolio might not be perfectly correlated with the market-index portfolio, we need to account for their mutual correlation in the determination of the optimal allocation. • The optimal combination of the active portfolio, A, with the passive portfolio, M, is a simple application of the construction of optimal risky portfolios from two components assets.

27. Portfolio construction: Optimal weight • then the optimal weight is the relative advantage of portfolio A as measured by the ratio: α/[Rm-rf], divided by the disadvantage of A, that is the ratio [σA]/[σM] • optimal weights are found using the usual optimization procedure • see also extension in the Black-Litterman model

28. Passive investment: index replication • Index replication refers to a low-cost mechanical investment process designed to gain exposure to either the broad equity market, or a segment characterized by country, region, market capitalization, sector or some other characteristic like style (growth/value stocks) or hedge funds returns. • In practical terms, an index fund is created by replicating a benchmark or index relevant to the target market or subset

29. Index replication • Index replication objective: minimizing the tracking error of the fund to the benchmark index. There coexist several methodologies. • Perfect replication might be expensive and might be limited by the size of the mimicking fund, especially when the benchmark includes numerous or illiquid assets. • Synthetic replication (using derivatives) exhibits appealing properties. However it might be limited by the existence of derivatives in the segment of the market we seek to mimic. Also rolling over the contracts is not cost free. • Stratified sampling enables one to minimize the tracking error and the costs.

30. Stratified sampling • For replicating indexes with large number of stocks and/or illiquid stocks. Stratified sampling allows the portfolio manager to mimic the key characteristics of the index without having to fully replicate it. • The procedure starts with classifying the stocks of the index across some key characteristics (like size, industry, PE, growth etc..). • A matrix is created with cells representing combinations of the characteristics. An example of such cells would be the group of companies within the banking sector growing by more than 15%. A weight is then assigned for each cell in the matrix based on the total weight of the cell’s companies within the index. A stock is then selected from each cell and assigned the weight of that cell in the portfolio. • Stratified sampling reduces transaction cost but increases tracking imperfection. Increasing the number of dimensions in the matrix reduces tracking error which is due to imperfect replication, but increases transaction costs.

31. Statistic replication • Enables one to reproduce the statistical properties of one index (mean, variance, higher moments and correlation with assets). • Also applied to Hedge fund replication, see Kat and Palaro (2007). • Multi factor analysis might be use to replicate hedge funds, especially their directional exposure. • http://www.hedgefundreplication.com • http://www.fundcreator.com

32. Summary • Monitoring the portfolio is the day to day activity of the portfolio manager. • Rebalancing is a source of performance but only controlling for costs. • Active management depends on trading or forecasting skills and the near-efficiency of the market. • Otherwise, passive replication of indexes or strategies.