FIN 4514 Exam III Review Be familiar with the principals of mutual fund performance evaluation The two key points with performance evaluation The arithmetic mean is not a useful statistic in evaluating growth Dollars are more important than percentages Know how to compute the traditional performance measures o Sharpe measure vs Treynor measure The Treynor measure evaluates return relative to beta a measure of systematic risk Ignores unsystematic risk so appropriate for both individual securities and portfolios The Sharpe measure evaluates return relative to standard deviation a measure of total risk Includes unsystematic risk so only appropriate for well diversified portfolios Sharpe vs Treynor Example Over the last four months XYZ Stock had excess returns of 1 86 percent 5 09 percent 1 99 percent and 1 72 percent The standard deviation of XYZ stock returns is 3 07 percent XYZ Stock has a beta of 1 20 What are the Sharpe and Treynor measures for XYZ Stock Solution First compute the average excess return for Stock XYZ Solution cont d Next compute the Sharpe and Treynor measures o Jensen measure The Jensen measure stems directly from the CAPM The constant term should be zero Securities with a beta of zero should have an excess return of zero according to finance theory According to the Jensen measure if a portfolio manager is better than average the alpha of the portfolio will be positive Jensen measure example Assume that the average realized return of a portfolio is 20 per year the standard deviation of returns is 30 and the portfolio beta is 1 5 Furthermore the average return of Treasury bills over the same period is 5 per year and the average return on the market is 15 per year Solve for Alpha Jensen measure in the following formula R Rf i Rm Rf R Rf i Rm Rf 0 20 0 05 1 5 0 15 0 05 0 0 Be prepared to calculate the volume weighted average price Portfolio managers want to minimize the impact of their trading on share price A buy order increases demand and price Portfolio managers frequently take the opposite position in the pre market trading Volume weighted average price equals the ratio of the dollar transaction volume to the share volume over a particular time period Volume weighted average example An institutional investor purchases shares of ABC stock in the following separate batches 12 000 shares at 46 58 8 000 shares at 46 53 and 15 000 shares at 46 47 What is the volumeweighted average price Dollar Transaction Volume 12 000 46 58 8 000 46 53 15 000 46 47 Solution 1 628 250 Share Volume 12 000 8 000 15 000 35 000 VWAP Dollar Transaction Volume Share Volume 1 628 250 35 000 46 5 Know how to compute the implementation shortfall Implementation shortfall is the difference between the value of a on paper theoretical portfolio and the actual portfolio purchased On paper portfolio is based upon price of last reported trade Actual purchases are likely to lead to higher costs due to Commissions Bid Ask Spread the prior trade may have been at the bid price while your trade will be at the ask price Market trend are prices moving higher Liquidity impact your demand may exceed the number of shares available at a lower price Implementation Shortfall Example You purchase 50 shares of XYZ stock The last reported trade was executed at 34 59 However your trading account reports a total transaction price of 1 745 What is the implementation shortfall Solution Value of On Paper Portfolio 50 34 59 1 729 50 Implementation Shortfall Actual Portfolio Value Value of On Paper Portfolio 1 745 1 729 50 15 or 0 31 per share Be familiar with performance measures that can be used in the presence of cash deposits and withdrawals o Daily valuation method The daily valuation method Calculates the exact time weighted rate of return Is cumbersome because it requires determining a value for the portfolio each time any cash flow occurs Might be interest dividends or additions to withdrawals from the fund o Modified BAI method The modified BAI method Approximates the internal rate of return for the investment over the period in question Can be complicated with a large portfolio that might conceivably have a cash flow every day o Approximate Method Proposed by the American Association of Individual Investors Note Do not need to know how to compute the above 3 methods just know them conceptually Know how to measure performance when options are involved o Incremental risk adjusted return IRAR The incremental risk adjusted return IRAR is a single performance measure indicating the contribution of an options program to overall portfolio performance A positive IRAR indicates above average performance A negative IRAR indicates the portfolio would have performed better without options The IRAR calculation IRAR example The Sharpe measure of an optioned portfolio is 0 254 while the Sharpe measure of the corresponding unoptioned portfolio is 0 148 The standard deviations of the optioned and unoptioned portfolios are 0 253 and 0 368 respectively What is the incremental risk adjusted return from options Solution IRAR SHo Shu o 0 254 0 148 0 253 0 027 2 7 o Residual option spread ROS The residual option spread ROS is an alternative performance measure for portfolios containing options A positive ROS indicates the use of options resulted in more terminal wealth than only holding the stock A positive ROS does not necessarily mean that the incremental return is appropriate given the risk ROS example Assume the quarterly return relatives for an optioned portfolio are 1 05 1 02 0 98 and 1 03 and the quarterly return relatives for the corresponding unoptioned portfolio are 1 03 0 99 0 95 and 1 02 What is the residual option spread Given an initial investment of 100 000 what is the dollar differential Left half of the equation 1 05 1 02 0 98 1 03 1 081 Right half of the equation 1 03 0 99 0 95 1 02 0 98 ROS 1 081 0 988 0 093 final answer If also asked to compute for the dollar differential like in this example then Dollar Differential Initial Investment ROS 100 000 0 093 9 300 Understand the function of the commodity futures market If suppliers and future buyers of a commodity could not agree on the future price of the commodity today There would be added price risk The price to the consumer would be significantly higher The basic function of the commodity futures market is to transfer risk from the hedger to the speculator The speculator assumes the risk because of the opportunity for profit Be familiar with the handling of