CHAPTER EIGHTEEN PORTFOLIO PERFORMANCE EVALUATION 1 MEASURES OF

CHAPTER EIGHTEEN PORTFOLIO PERFORMANCE EVALUATION 1

MEASURES OF RETURN • MEASURES OF RETURN – complicated by addition or withdrawal of money by the investor – percentage change is not reliable when the base amount may be changing – timing of additions or withdrawals is important to measurement 2

MEASURES OF RETURN • TWO MEASURES OF RETURN – Dollar-Weighted Returns • uses discounted cash flow approach • weighted because the period with the greater number of shares has a greater influence on the overall average 3

MEASURES OF RETURN • TWO MEASURES OF RETURN – Time-Weighted Returns • used when cash flows occur between beginning and ending of investment horizon • ignores number of shares held in each period 4

MEASURES OF RETURN • TWO MEASURES OF RETURN – Comparison of Time-Weighted to Dollar. Weighted Returns • Time-weighted useful in pension fund management where manager cannot control the deposits or withdrawals to the fund 5

MAKING RELEVANT COMPARISONS • PERFORMANCE – should be evaluated on the basis of a relative and not an absolute basis • this is done by use of a benchmark portfolio – BENCHMARK PORTFOLIO • should be relevant and feasible • reflects objectives of the fund • reflects return as well as risk 6

THE USE OF MARKET INDICES • INDICES – are used to indicate performance but depend upon • the securities used to calculate them • the calculation weighting measures 7

THE USE OF MARKET INDICES • INDICES – Three Calculation Weighting Methods: • price weighting – sum prices and divided by a constant to determine average price – EXAMPLE: THE DOW JONES INDICES 8

THE USE OF MARKET INDICES • INDICES – Three Calculation Weighting Methods: • value weighting (capitalization method) – price times number of shares outstanding is summed – divide by beginning value of index – EXAMPLE: » S&P 500 » WILSHIRE 5000 » RUSSELL 1000 9

THE USE OF MARKET INDICES • INDICES – Three Calculation Weighting Methods: • equal weighting – multiply the level of the index on the previous day by the arithmetic mean of the daily price relatives – EXAMPLE: » VALUE LINE COMPOSITE 10

ARITHMETIC V. GEOMETRIC AVERAGES • GEOMETRIC MEAN FRAMEWORK GM = (P HPR)1/N - 1 where P = the summation of the product of HPR= the holding period returns n= the number of periods 11

ARITHMETIC V. GEOMETRIC AVERAGES • GEOMETRIC MEAN FRAMEWORK – measures past performance well – represents exactly the constant rate of return needed to earn in each year to match some historical performance 12

ARITHMETIC V. GEOMETRIC AVERAGES • ARITHMETIC MEAN FRAMEWORK – provides a good indication of the expected rate of return for an investment during a future individual year – it is biased upward if you attempt to measure an asset’s long-run performance 13

RISK-ADJUSTED MEASURES OF PERFORMANCE • THE REWARD TO VOLATILITY RATIO (TREYNOR MEASURE) – There are two components of risk • risk associated with market fluctuations • risk associated with the stock – Characteristic Line (ex post security line) • defines the relationship between historical portfolio returns and the market portfolio 14

TREYNOR MEASURE • TREYNOR MEASURE – Formula where arp = the average portfolio return arf = the average risk free rate bp = the slope of the characteristic line during the time period 15

TREYNOR MEASURE THE CHARACTERISTIC LINE arp SML bp 16

TREYNOR MEASURE • CHARACTERISTIC LINE – slope of CL • measures the relative volatility of portfolio returns in relation to returns for the aggregate market, i. e. the portfolio’s beta • the higher the slope, the more sensitive is the portfolio to the market 17

TREYNOR MEASURE THE CHARACTERISTIC LINE arp SML bp 18

THE SHARPE RATIO • THE REWARD TO VARIABILITY (SHARPE RATIO) – measure of risk-adjusted performance that uses a benchmark based on the ex-post security market line – total risk is measured by sp 19

THE SHARPE RATIO • SHARPE RATIO – formula: where SR = the Sharpe ratio sp = the total risk 20

THE SHARPE RATIO • SHARPE RATIO – indicates the risk premium per unit of total risk – uses the Capital Market Line in its analysis 21

THE SHARPE RATIO arp CML sp 22

THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE • BASED ON THE CAPM EQUATION – measures the average return on the portfolio over and above that predicted by the CAPM – given the portfolio’s beta and the average market return 23

THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE • THE JENSEN MEASURE – known as the portfolio’s alpha value • recall the linear regression equation y = a + bx + e • alpha is the intercept 24

THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE • DERIVATION OF ALPHA – Let the expectations formula in terms of realized rates of return be written – subtracting RFR from both sides 25

THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE • DERIVATION OF ALPHA – in this form an intercept value for the regression is not expected if all assets are in equilibrium – in words, the risk premium earned on the jth portfolio is equal to bj times a market risk premium plus a random error term 26

THE JENSEN MEASURE OF PORTFOLIO PERFORMANCE • DERIVATION OF ALPHA – to measure superior portfolio performance, you must allow for an intercept a – a superior manager has a significant and positive alpha because of constant positive random errors 27

COMPARING MEASURES OF PERFORMANCE • TREYNOR V. SHARPE – SR measures uses s as a measure of risk while Treynor uses b – SR evaluates the manager on the basis of both rate of return performance as well as diversification 28

COMPARING MEASURES OF PERFORMANCE – for a completely diversified portfolio • SR and Treynor give identical rankings because total risk is really systematic variance • any difference in ranking comes directly from a difference in diversification 29

CRITICISM OF RISK-ADJUSTED PERFORMANCE MEASURES • Use of a market surrogate • Roll: criticized any measure that attempted to model the market portfolio with a surrogate such as the S&P 500 – it is almost impossible to form a portfolio whose returns replicate those over time – making slight changes in the surrogate may completely change performance rankings 30

CRITICISM OF RISK-ADJUSTED PERFORMANCE MEASURES • measuring the risk free rate • using T-bills gives too low of a return making it easier for a portfolio to show superior performance • borrowing a T-bill rate is unrealistically low and produces too high a rate of return making it more difficult to show superior performance 31