Title LM06 Analysis of Active Portfolio Management IFT Notes.pdf ✅

LM06 Analysis of Active Portfolio Management 2023 Level II Notes © IFT. All rights reserved 2 1. Introduction The underlying premise of active portfolio management is that financial markets are not perfectly efficient and investors can construct active portfolios to generate active returns. Active portfolios are constructed by holding securities of a benchmark in weights different than the benchmark. This reading covers:  The mathematics of value added through active management and related concepts such as active weights, relative returns, and performance attribution systems.  How to use the Sharpe ratio and information ratio to measure risk-adjusted value.  The fundamental law of active management: Understand how skill, breadth of application, aggressiveness, and the constraints in portfolio construction combine to affect value added.  Examples of active portfolio management strategies in equity and fixed income markets.  Practical limitations of the fundamental law. 2. Active Management and Value Added The goal of active portfolio management is to add value by outperforming a passively managed benchmark portfolio. Investing in the benchmark portfolio is called passive investing. If the investor outperforms the benchmark portfolio, value added is positive. If the investor underperforms the benchmark portfolio, value added is negative. 2.1 Choice of Benchmark The choice of benchmark is important as the performance of the active portfolio is measured relative to the benchmark. A benchmark must have the following three qualities:  The benchmark is representative of the assets from which the investor will select.  Positions in the benchmark portfolio can actually be replicated at low cost.  Benchmark weights are verifiable ex-ante, and return data are timely ex-post. In other words, the weights of all constituent securities should be known upfront and the returns are known at the end of the period. For example, if the investor’s portfolio is composed of large cap US stocks, then an appropriate benchmark would be S&P 500 which meets all three qualities listed above. The return on a benchmark portfolio, RB, is a function of the weights of each security in the benchmark portfolio and their returns: RB = ∑ wB,iRi N i=1 where: wB,i = the benchmark weight of security i
LM06 Analysis of Active Portfolio Management 2023 Level II Notes © IFT. All rights reserved 3 Ri= the return on security i N = number of securities Similarly, the return on an actively managed portfolio is a function of the weights of each security in the active portfolio and their returns: RP = ∑ wP,iRi N i=1 where: wP,i = the weight of the i securities held in the portfolio 2.2 Measuring Value Added Active return: Active return is the value added by active management. The active return of a portfolio, RA, is given by: RA = RP– RB Note that this is not the same as the managed portfolio’s alpha. The portfolio’s alpha is calculated after adjusting for the portfolio’s risk relative to the benchmark: αP = RP – βPRB Active weights: The value addition in an actively managed portfolio comes from active weights. Active weight is the difference between a security’s weight in an actively managed portfolio and its weight in the benchmark. Overweighted securities have positive active weights. Underweighted securities have negative active weights. The sum of active weights of all securities in the portfolio must be zero. Δwi = wP,i – wB,i where Δwi = active weights We can express the value added as the sum product of active weights and active security returns: RA = ∑ Δwi RAi N i=1 where: RAi = Ri − RB = the active return of each security. This equation can be used to calculate the contribution to value added from each segment. Example: Consider a benchmark that consists of just two assets: 60% stocks and 40% bonds. The active portfolio consists of 70% stocks and 30% bonds. The ex-post returns on stocks and bonds are 14% and 2% respectively. What is the active return and contribution from each segment? Portfolio return = 0.7 ∗ 0.14 + 0.3 ∗ 0.02 = 10.4% Benchmark return = 0.6 ∗ 0.14 + 0.4 ∗ 0.02 = 9.2%
LM06 Analysis of Active Portfolio Management 2023 Level II Notes © IFT. All rights reserved 4 Active return = 10.4% − 9.2% = 1.2% Contribution to active return from stocks = active weight of stocks * active return of stocks = 0.1 ∗ (0.14 − 0.092) = 0.005 Contribution to active return from bonds = active weight of bonds * active return of bonds = −0.1 ∗ (0.02 − 0.092) = 0.007 Example: Value Added and Country Equity Markets (This is based on Example 1 of the curriculum.) The following information is provided for an actively managed portfolio and its benchmark: Country Benchmark Weight Portfolio Weight 2013 Return United Kingdom 22% 16% 20.7% Japan 21% 14% 27.3% France 10% 8% 27.7% Germany 9% 24% 32.4% Other Countries 38% 38% 18.8% 1. Which countries have the largest overweight and largest underweight in the managed portfolio compared with the benchmark portfolio? What are the active weights for these two countries? 2. Using active weights and total returns, what was the value added of the managed portfolio over the benchmark portfolio in the calendar year 2013? Solution to 1: First, construct an additional column for active weights: Country Benchmark Weight Portfolio Weight 2013 Return Δwi United Kingdom 22% 16% 20.7% -6% Japan 21% 14% 27.3% -7% France 10% 8% 27.7% -2% Germany 9% 24% 32.4% +15% Other Countries 38% 38% 18.8% 0% Germany has the largest overweight at 24 – 9 = +15%, and Japan has the largest underweight at 14 – 21 = –7%. Solution to 2: The value added is –0.06(20.7) – 0.07(27.3) – 0.02(27.7) + 0.15(32.4) = 1.2%. 2.3 Decomposition of Value Added In the previous section, we made a simple assumption that all the active return of an