JAN24 2022 FI4000 Spring2022 Exercises In class Exercises for Breakout rooms 1 Solutions 1 A fund begins with 10 million and reports the following monthly results MONTH 1 2 3 3 2 5 8 0 4 Net inflows end million HPR Compute the i Arithmetic ii Time weighted and iii weighted average monthly returns Solution See Concept Check 1 Solution at end of Chapter 5 in textbook 2 Sharpe ratio and capital allocation a To estimate the Sharpe ratio of a portfolio from a history of asset returns we use the difference between the simple arithmetic average rate of return and the T bill rate Why not use the geometric average b When estimating a Sharpe ratio would it make sense to use the average excess real returns that accounts for inflation c You have jus decided upon your capital allocation for the next year when you realize that you have underestimated both the expected return and the standard deviation of your risky portfolio by 4 Will you increase decrease or leave unchanged your allocation to risk free T bills Solutions a The geometric return represents a compounding growth number and will artificially inflate the annual performance of the portfolio b The excess return on the portfolio will be the same as long as you are consistent you can use either real rates for the returns on both the portfolio and the risk free asset or nominal rate for each Just don t mix and match So the average excess return the numerator of the Sharpe ratio will be unaffected Similarly the standard deviation of the excess return also will be unaffected again as long as you are consistent c Decrease Typically standard deviation exceeds return Thus an underestimation of 4 in each will artificially decrease the return per unit of risk To return to the proper risk return relationship the portfolio will need to decrease the amount of risk free investments 3 XYZ stock price and dividend history are as follows Year Beginning of Year Price Dividend paid at Year end 2010 2011 2012 2013 100 110 90 95 4 4 4 4 An investor buys three shares of XYZ at the beginning of 2010 buys another two shares at the beginning of 2011 sells one share at the beginning of 2012 and sells four remaining shares at the beginning of 2013 a What are the arithmetic and geometric average time weighted rates of return for the investor b What is the weighted rate of return Hint Carefully prepare a chart of cash flows for the four dates corresponding to the turns of the year for January 1 2010 to January 1 2013 Calculate internal rate of return IRR using either your calculator excel spreadsheet or trial and error Solutions a Time weighted average returns are based on year by year rates of return Year 2010 2011 2011 2012 2012 2013 Return Capital gains Dividend Price 110 100 4 100 0 14 or 14 00 90 110 4 110 0 1455 or 14 55 95 90 4 90 0 10 or 10 00 Arithmetic mean 0 14 0 1455 0 10 3 0 0315 or 3 15 1 Geometric mean 0 0233 or 2 33 b Net Cash Flow 1 1 2010 300 1 1 2011 208 Date 1 1 2012 110 1 1 2013 396 Time Net Cash flow 0 1 2 3 300 208 110 396 Explanation Purchase of three shares at 100 per share Purchase of two shares at 110 plus dividend income on three shares held Dividends on five shares plus sale of one share at 90 Dividends on four shares plus sale of four shares at 95 per share The dollar weighted return is the internal rate of return that sets the sum of the present value of each net cash flow to zero 0 300 Dollar weighted return Internal rate of return 0 1661