Portfolio Management

1. Portfolio Management Grenoble Ecole de Management Msc Finance 2011

2. Learning Objectives Mastering the principles of the portfolio management process: • Evaluating Portfolio Performance

3. Portfolio Management Evaluating Portfolio Performance

4. Evaluating Performance • Ex post quality control check. • Part of the feedback step of the investment management process. It should be documented in the IPS. • Analytic techniques give insights about the past returns, sources of past returns and their consistency.

5. The three components of performance evaluation For any portfolio, we want to answer the following questions: What was the portfolio’s performance ? Why did the portfolio produce the observed performance ? Is the portfolio’s performance due to luck or skill ?

6. The three components of performance evaluation For any portfolio, we want to answer the following questions: What was the portfolio’s performance ? This is performance measurement Why did the portfolio produce the observed performance ? This is performance attribution Is the portfolio’s performance due to luck or skill ? This is performance appraisal which attempts to draw conclusions concerning the quality (magnitude and consistency) of the portfolio’s relative performance.

7. Performance measurement (first step) • Performance measurement is just a component of performance evaluation. • Performance measurement is the procedure of calculating returns for a portfolio. • Performance evaluation encompasses broader and much more complex task of placing those investment results in the context of the portfolio’s investment objectives.

8. Performance measurement Performance measurement withoutintraperiod external cash flows. If there is no cash flow in the intraperiod, the return calculation is as simple as: with MV the market value with MV the market value. In the case of a portfolio with initial market value of EUR 1.000.000 and final market value of EUR 1.080.000, the return is 8%

9. Performance measurement Performance measurement with intraperiod external cash flows. Customers add and subtract cash to and from their managers’ portfolios at the beginning or at the end period (especially for daily funds). For inflows For outflows

10. The time weighted rate of return • When cash flows do not match with the beginning or the end of a period (for monthly or quarterly fund), one has to use the TWR. • The TWR calculation requires the portfolio to be valued every time an external cash flow occurs. • We need to create subperiod rate of return in which cash is added at the end or beginning period.

11. The time weighted rate of return The portfolio received two cash flows during month t: a contribution of EUR 30.000 on day 5 a contribution of 20.000 on day 16. We have a daily pricing system that provides us with values of the account of 1.045.000 and 1.060.000 on days 5 and 16 of the month, respectively. Final value is 1.080.000. We can calculate 3 separate subperiod returns using the rate of return computation:

12. The time weighted rate of return The TWR derives its name from the fact that each subperiod return within the full evaluation period receives a weight proportional to the length of the subperiod relative to the length of the full evaluation period.

13. The money weighted rate of return The money weighted rate of return MWR measures the compound growth rate in the account over the evaluation period. It is also called internal rate of return. m = number of time units in the evaluation period Cfi = the ith cash flow L(i) number of time units by which the ith cash flow is separated from the beginning of the evaluation period.

14. The money weighted rate of return The MWR of the preceding example is found solving the following equation: There exists no closed-form solution for R. R must be solved iteratively. In this case r = 0.0009536. this is the portfolio’s daily rate of return during the month. In a monthly basis MWR is

15. TWR versus MWR • MWR represents the average growth rate of all money invested in a portfolio • TWR represents the growth of a single unit of money invested in the portfolio. • The MWR is sensitive to the size and timing of external cash flows while the TRW is unaffected by these flows. • Under normal conditions, they will produce similar returns 2.9% and 2.92% in the example. However when flows are large compared to the portfolio size, or performance is fluctuating significantly, returns may be different.

16. TWR and MWR • The TWR is used more often than MRW. Rates of return are typically reported on an annualized basis. • However the TWR may be approximated by calculating the MWR over reasonably frequent time intervals for control purpose.

17. Benchmarks • By its nature, performance evaluation is a relative concept. • Benchmarks give insights on how alternative uses of money would have performed if exposed to similar risks. • The benchmark is a passive representation of the manager’s investment style. • A benchmark is a collection of securities or risk factors and associated weights that represents an asset category or manager’s investment process.

18. Benchmarks • The benchmark is a key element of the IPS. • A valid benchmark has the following characteristics : • Unambiguous • Investable • Measurable • Appropriate • Specified in advance • The properties listed formalize intuitive notions of what constitutes a fair and relevant performance comparison. • It becomes the basis for evaluating the success of the manager’s investment management efforts.

19. Usual benchmarks • Absolute.An absolute return can be a return objective. Examples include an actuarial rate of return assumption. But as absolute return objectives are not investable alternatives they do not satisfy the main criteria. • Manager universes.Peer group comparison. Respect only the measurability criteria. • Broad market index.S&P 500, Wilshire 5000, US BIG (broad investment grade) for fixed income. They satisfy many properties of valid benchmarks if they are appropriately used.

20. Benchmarks • Style indexes.Specific portion of an asset category. Large capitalization, small capitalization, value, growth... • Factor model based.Using the beta of the portfolio, returns expectations are linear to the calculated beta. • Custom security based. The manager will select those securities that represent the most attractive investment opportunities. Concentration on unique risk.

21. Benchmarks • The value of an index is the result of a calculation. A distortion exists between the value of the index and the cost to buy the index. • Dow Jones Industrial Average (DJIA), S&P500, Nasdaq100, Wilshire5000, Russel, FTSE, MSCI, Nikkei

22. Benchmarks: DJIA dividend reinvested

23. Benchmarks • Index may be cap weighted or equally weighted. • Cap weighted index tend to concentrate the risk over a small number of large stocks. Therefore they might have lower volatility. • They might create momentum effects. Higher performing stocks being overbought. It is the opposite for equally weighted index.

24. Benchmarks: S/P EQW vs Cap W

25. Performance attribution (2nd step) • Identification and quantification of sources of differential returns between the portfolio and its benchmark. • There is no one single correct approach. • We identify macro attribution and micro attribution

26. Impact equals weight times return Sources of relative returns: Selecting superior (or avoiding inferior) performing assets Owning the superior (inferior) performing assets in greater (less) proportions than are held in the benchmark. The fundamental rule prevails that impact equals (active) weight times return.

27. Impact equals weight times return Consider a business that sells cars. Its total revenue is determined by the following formula: Revenue = Price (P) * Quantity sold (Q) This year revenue R has risen. Why ? We need a performance attribution. The increase in revenues can be attributed to changes in the unit prices or quantity sold or both.

28. Impact equals weight times return • The old revenue was equal to P1*Q1. the new revenue is equal to P2*Q2. It is due in part to : • an increase in price (P2-P1)*Q1 • an increase in quantity sold (Q2-Q1)*P1 • the interaction of both variables (P2-P1)*(Q2-Q1). • With the identity between the two sides of the equation: • (P2*Q2) – (P1*Q1) = (P2-P1)*Q1 + (Q2-Q1)*P1 + (P2-P1)*(Q2-Q1) • The change in quantity is roughly analogous to a difference in weights while the change in price represents the difference in returns between securities held in the portfolio and the benchmark.

29. Micro attribution. Over a given evaluation period, the portfolio will produce a return that is different from the return on the benchmark: this is the manager’s value added or active return. Manager’s value added = Portfolio’s return – Benchmark’s return

30. Micro attribution. Where wpi and wbi are the proportions of the portfolio and benchmark, respectively invested in security i, ri is the return on security i, and n is the number of securities. Then for an analysis security by security:

31. Micro attribution. • The large number of securities in a well diversified portfolio makes the impact of any individual security on portfolio returns largely uninteresting. • A more productive form of micro attribution involves allocating the value added return to various sources of systematic returns. • Most micro attribution are based on factor model of returns.

32. Sector weighting-Stock selection. The return can be expressed as the difference between the weighted average return on the economic sectors in the portfolio and the benchmark: With wpj the portfolio weight of sector j, wbj the benchmark weight of sector j, rpj the portfolio return of sector j, rbj the benchmark return of sector j, s is the number of sectors.

33. Sector weighting-Stock selection. The preceding equation can be rearranged to form the following relationship: 1 is pure sector allocation. It assumes that within each sector the manager held the same securities as the benchmark and in the same proportions. 2 is allocation/selection interaction. Joint effect of the portfolio managers’ and security analysts’ decisions to assign weights to both sectors and individual securities. It equals the difference between the weight of the portfolio in a given sector and the portfolio’s benchmark for that sector, times the difference between the portfolio’s and the benchmarks returns in that sector, summed across all sectors.

34. Sector weighting-Stock selection. 3 is within sector selection. return implicitly assumes that the manager weights each sector in the portfolio in the same proportion as in the overall benchmark, although within the sector the manager may hold securities in different from benchmark weights. Thus, the impact on relative performance is now attributed only to the security selection decisions of the manager.

35. Sector weighting-Stock selection. The same attribution might be performed on risk, enabling one to decompose the risk of the portfolio between risk due to sector allocation (1), within sector selection (3) and interaction (2). Is the tracking error of the portfolio (sd-error of the difference between the return of the portfolio S and the benchmark)

36. Sector weighting-Stock selection. The health care industry sector represents 10% of a given benchmark (wb1 = 10%). The manager has decided to allocate 12% of its portfolio to this sector (wp1 = 12%). The return of the health care industry sector as weighted in the benchmark is rbj = 5%, it is rpj = 7% in the manager portfolio. The overall benchmark has a performance of rb = 3%.

37. Fixed income attribution. • Factors are: • Changes in the level, slope and curvature of interest rates. • Sector quality effect • Security selection effect • Trading activity

38. Macro attribution overview Macro attribution concerns portfolio managers within the pool of management of the fund sponsor. It enables the sponsor to decide regarding manager selection. . Three sets of inputs constitute the foundation of macro attribution: Policy allocation. Benchmark portfolio returns. Fund returns, valuations and external cash flows. With these inputs in hand we can decompose the Fund’s performance from a macro perspective.

39. Policy allocations 6 levels of investment policy must be analyzed: Net contributions Risk free asset Asset categories Benchmarks Investment managers Allocation effects

40. Policy allocations Net contributions: as the performance of the fund is the difference in market value, the first line of performance attribution is the net cash flow contribution. Net cash flow over the period Risk free asset: part of the fund invested in risk free assets Asset category: performance attribution by categories With R the return of asset category (ac), rci the return of the ith category and wi its weight.

41. Policy allocations 4) Benchmarks Where ris is the incremental return contribution of the benchmark strategy, rbi is the return for the benchmark in asset category I, rci is the return on the ith asset category, wiis the policy weight assigned to the ithasset category, and A is the number of asset categories.

42. Net contributions Investment managers discern the impact of the managers’ active management decisions on the change of the funds’ value. where rajirepresents the actual return on the jthmanager’s portfolio within asset category I and the other variables are as defined previously. Allocation effects. By definition it is a reconciling factor, the difference between the fund’s ending value and the value calculated at the Investment Managers level.

43. Performance appraisal (third step) • Appraising manager investment skill. • We define investment skill as the ability to outperform an appropriate benchmark consistently over time. • It is the magnitude of the value added returns relative to the variability of value added returns that determines a manager’s skill.

44. Risk adjusted performance appraisal measures • three risk adjusted performance appraisal measures have become widely used: • Jensen’s alpha • Treynor ratio • Sharpe ratio

45. Ex post alpha Use the ex post security market line (SML) to form a benchmark for performance appraisal purposes. We can write: Ri is the return on the portfolio, rf the risk free rate and Rm the return on the market proxy. The estimate of alpha can be interpreted as the differential return of the portfolio compared to the return required to compensate for the systematic risk (beta). The level of skills depends on the sign and value of alpha.

46. Ex post alpha The level of skills depends on the sign and value of alpha which measures the vertical distance to the SML. We seek managers with positive alpha: managers that have excess returns compared to the risk of their portfolios.

47. Treynor measure Use also the SML to form a benchmark. For any portfolio i: Ri is the mean return of portfolio I and rf is the risk free rate. Larger Treynor mean better investment skill. However there is no absolute reference. Treynor enables only to rank managers performances. and

48. Sharpe ratio The sharpe ratio compares excess returns to the total risk of the portfolio, where total risk is measured by the portfolio standard deviation of returns. Ri is again the mean return of the portfolio. The Sharpe ratio is based on the CML not the SML. Because the Sharpe ratio is based on a return differential, it represents the results of a self financing strategy. Sharpe ratio can be calculated against a benchmark. It is then called the information ratio. In this case, the numerator is the active return while the denominator is the tracking error, the volatility of the difference between the portfolio return and the benchmark return.

49. More complex measures The Sortino ratio measures the risk adjusted return of a portfolio considering only negative volatility as a measure of risk. where Ri is the mean return of the portfolio, T the target return and DR the downside risk or the square root of the portfolio return semivariance. Sterling ratio. Risk reward measure which compares excess returns to the average of the worst events volatility. Calmar ratio is the absolute version of the Sterling ratio (no -10%) Modified sharpe ratio: sharpe ratio with modified VAR as denominator.

50. Summary • performance measurement enables to quantify the portfolio returns. • performance attribution enables to determine the sources of over and under performances • performance appraisal enables to measure the quality (magnitude and consistency) of the portfolio returns