ABF305 Investment Management
Lecture 10
Reminder from last week: what you do not need to read in Chapter 23.
For Chapter 23, you do not need to read from page 809 ‘Credit risk in the swap market’ onwards. You also do not need to do the section on creating synthetic stock positions which is on pages 796 to 799.
Portfolio Performance Evaluation.
投资组合绩效评估。
Investment management is meaningless without some kind of measure with regards to well or how badly you are doing.
投资管理是没有意义的,没有某种措施方面好或如何不好你正在做的。
From a very basic point of view, a performance is evaluated in terms of the rate of return for the underlying investment.
从一个非常基本的角度来看,绩效评估相关投资的回报率。
Example of rate of return:
回报率的例子:
If you have bought a share for $50 and held it for one year during which time you received a dividend of $2 for the share and you sold it for $53 at the end of one year, then in terms of your underlying investment your rate of return will be 10%, being the $2 dividend and the $3 capital gain in price divided by the underlying investment 5/50 = 10%.
Example of internal rate of return:
内部盈利率的例子
Another way to represent the return rate is to rephrase things in terms of present values. So we could say that the initial investment of $50 could be represented by the dividend + the sale price/(1+r) for which you solve for.
The internal rate of return can be used for differing cash flows. For example, let us say that you purchased a second share for $53 in the second year in addition to the first share for $50 and after two years you sold them both for $54. You received the $2 dividend in the meantime each year.
Another term for the IRR is the dollar-weighted rate of return. Specifically, rates of return can be time weighted or dollar weighted. The difference is that for dollar-weighted rates of return, it takes into account the amount invested where as for time-weighted returns (rG) the return for each period is given equal weighting regardless of the amount involved.
For our previous example, a time-weighted return would have rendered a rate of 7.83% which would be calculated as follows:
The rate of return for the first year is determined as:
The rate of return for the second year is determined as:
Portfolio performance needs to be risk-adjusted.
Three methods used in finance literature to evaluate risk-adjusted performances are:
The Sharpe ratio.
The Treynor measure.
The Jensen’s measure.
The Treynor measure:
特雷诺指标
The Treynor measure is similar to the Sharpe ratio in that it gives a measure of the excess return per unit of risk, but it uses systematic risk instead of total risk as the denominator. So instead of using the standard deviation of the return, the portfolio Beta is used.
The Jensen’s measure:
The Jensen’s measure is the average return on the portfolio over and above that predicted by the CAPM, given the portfolio’s beta and the average market return. The Jensen measure is denoted by:
The portfolio’s alpha value is the intercept for the linear regression where the excess returns to a market portfolio and the market index are respectively, the dependent and the independent variables: rp –rf = α+β(rm – rf) + εp
The information ratio:
信息比率
There is also a fourth measure used by financial markets which is the information ratio.
The ratio divides the alpha of the portfolio by the nonsystematic risk of the portfolio called ‘tracking error’ in the industry. The information ratio measures abnormal return per unit of risk that in principle could be diversified away by holding a market index portfolio.
Each of these four performance metrics have the same underlying principal which is that the portfolio return is measured in terms of risk. They differ, however, in terms of the risk, namely for the Sharpe ratio the risk is total risk, for the Treynor measure it is systematic risk, for the Jensen measure risk is denoted in terms of the CAPM, and for the information ratio, the risk is non-systematic risk.
The appropriate performance measure depends on the role of the portfolio to be evaluated. Appropriate performance measures are as follows:
Sharpe ratio: when the portfolio represents the entire investment fund.
Information ratio: when the portfolio represents the active portfolio to be optimally mixed with the passive portfolio.
Treynor or Jensen measures: when the portfolio represents a sub-portfolio of many.
Modigliani and Modigliani M-Squared measure of performance.
We saw with the Sharpe Ratio that we arrived at a ratio for the portfolio and one for the market. What the Modigliani’s suggested was to standardize both measures.
M² = rp - rm
Performance evaluation when the investment changes:
This is demonstrated by Example 24.3 in your textbook.
In this example it shows what happens when an actively managed portfolio which changes from a low-risk strategy to a high-risk strategy is not considered and as a consequence the Sharpe ratio provides a misleading result.
The example will be discussed in the lecture.
The measurement of market timing
To indicate timing ability, Treynor and Mazuy proposed that the slope as represented by the security characteristic line would be higher. They proposed that such a line could be estimated by adding a quadratic term to the usual index model.
rp –rf = α+β(rm – rf) + c(rm – rf)² + εp
If c is positive, it is argued there is evidence of market timing because the c(rm – rf)² into the linear index model will make the characteristic line steeper as rm – rf is larger.
Style analysis
风格分析
Style analysis is an attempt to explain the variability in the observed returns to a security portfolio in terms of the movements in the returns to a series of benchmark portfolios designed to capture the essence of a particular security characteristic such as size, value, and growth. (Reilly and Brown, ‘Investment Analysis and Portfolio Management’ 8th Edition).
风格分析是试图解释所观察到的安全组合用来捕捉一个特定的安全特性,如大小,价值和成长的本质了一系列的基准投资组合的回报率变动的变异。 (Reilly和布朗,“投资分析与组合管理”第8版)。
Value investing is when fund managers try to find ssecurities which are priced well below their intrinsic value. They then buy and hold those securities until their price is in line with their intrinsic value. Value investing is the most conservative of the mutual fund styles because in general, such companies are out of favour with the market for some reason but are not what one would consider "distressed."
价值投资时,基金管理者试图找到它的价格远远低于其内在价值安全的。然后,他们购买并持有这些证券,直至他们的价格是符合其内在价值。价值投资共同基金的风格是最保守的,因为在一般情况下,这类公司由于某种原因,与市场的青睐,但都没有什么人会考虑“心疼”。
Growth investing is considered a moderate form of the mutual fund styles. Growth investors find securities that are in the growth stage of their life cycle or are poised to grow at a relatively rapid rate, thus providing an acceptable risk-adjusted return on investment (ROI). They will hold these companies' securities as long as they remain in the growth stage and there are no negative changes in the companies' fundamentals.
成长型投资共同基金的风格被认为是一种温和的形式。成长型投资者发现证券,在其生命周期的成长阶段或正准备在一个相对较快的速度增长,从而提供了一个可接受的风险调整后的投资回报率(ROI)。只要他们仍处于成长阶段,公司的基本面,有没有负面的变化,他们将持有这些公司的证券。
Blend investing is a mutual fund style that employs a combination of both value investing and growth investing.
The whole point of identifying the style of a fund manager is that it is arguably a fairer representation of how to evaluate a portfolio performance.
Style analysis is related to the basic concept of risk adjusted return.
This concept was introduced by Sharpe and his idea was to regress fund returns on indexes representing a range of asset classes. The regression coefficient on each index would then measure the fund’s implicit allocation to that “style”. In addition to the ‘style’, Sharpe also included in his regression explanatory variables for the size of firm. The market capitalization is a representation of the firm size.
Superior performance depends on the ability to be in the ‘right’ securities at the right time. It can be decomposed into (1) timing ability, and (2) section ability. This decomposition is possible through performance attribution procedures. The attribution method explains the difference in returns between a managed portfolio, P, and a selected benchmark portfolio, B, called the bogey.
Please see pages 851 -856 for a detailed example of this procedure. It will be explained in the lecture.
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