1. Finance 300 Financial Markets Lecture 2 Professor J. Petry, Fall, 2002© http://www.cba.uiuc.edu/jpetry/Fin_300_fa02/ http://webboard.cites.uiuc.edu/

2. 2 Chapter II-Portfolio Theory 1.Measuring Portfolio Risk & Return 2.Diversification 3.Capital Asset Pricing Model (CAPM) 4.Arbitrage Pricing Theory (APT)

3. 3 Measuring Portfolio Returns Holding Period Rate of Return (HPR) Cash Flow Adjusted Rate of Return (CFA) Statistical (arithmetic) Rate of Return Time-Weighted (geometric) Rate of Return Internal Rate of Return (IRR)

4. 4 Holding Period Rate of Return HPR = Holding Period Return V 1 = Ending value V 0 = Beginning value Used to calculate the total return from an investment over any set time period (day, month, year, 3 weeks). Includes all sources of income (capital gain, dividends).

5. 5 Examples HPR with V 0 of 1,000,000 and V 1 of 1,300,000 R = 1,300,000/1,000,000 = 1.30 = 1 + 30% HPR with V 0 of 200,000 and V 1 of 134,000 R = 134,000/200,000 = 0.67 = 1 - 33% HPR with V 0 of 2,000,000 and V 1 of: 2,124,770R = 1,843,748R = 2,000,000R =

6. 6 Cash Flow Adjusted Rate of Return V 0 = Beginning value V 1 = Ending value date = number of days prior to cash flow timing; if cash flow was during 3 rd, date = 3. Monthly CFA used to correct returns for entrance and exit of investable resources under management.

7. 7 Examples HPR of 1 month investment with V 0 of 2,000,000 and V 1 of 2,575,000. R = 1 + 28.75% And if 500,000 was invested on the last day of the month? R = 1 + 3.75%

8. 8 Examples-CFA Rate of Return Three investment managers (Ralph, Joe & Madonna) start the month with 250,000. Each is given 150,000 more to invest (Ralph at the outset, Joe on the 20th and Madonna on the 30th). They ended with 412,500; 410,000, and 410,050 respectively. Who should you invest with?

9. 9 Cash Flow Adjusted Rate of Return When there are many cash flows spread throughout the month or they are small relative to the value of the portfolio, this formula is simplified to assume the flows occur mid-month.

10. 10 Cash Flow Adjusted Rate of Return Many investments yield dividend payments, which are often reinvested by the portfolio manager. We would NOT consider this a cash flow which should be adjusted in the fashion described by CFA return. Why not? Use the data for Ralph, Joe and Madonna in this simplified formula. How different are your answers from before? Which makes each portfolio manager look better?

11. 11 Statistical (arithmetic) Rate of Return Assumes a constant amount reinvested every period. When looking at the return on an investment without reference to when an investor bought, sold or reinvested money, this is the appropriate method to use. (i.e.starting fresh every period) Single best forecast for future one-period returns Does not consider compounding Uses arithmetic total and mean to perform calculations.

12. 12 Examples-Statistical Rate of Return Fred earned the following returns: Jan 3.4% Feb 5.2% March-3.5% Fred’s total return = 3.4 + 5.2 - 3.5 = 5.1% for the quarter Fred’s average return = 5.1 / 3 = 1.7% per month Fred’s annualized return is 1.7 x 12 = 20.4% If Billy Bob earned 13.4% in Q1, and -5.0% in Q2, what was his average return, semi-annual return and annualized returns?

13. 13 Time-Weighted Rate of Return The time-weighted rate of return assumes that whatever amount you ended with last period, you reinvest at the beginning of this period. This is the method to use when tracking exactly the amount bought, sold, reinvested by a particular client. Referred to as “geometric”. Compounds, but doesn’t consider amount invested. Provides same result as HPR. Rudolph had returns of 3.3%, -2.5%, 5.0% in 1st quarter. Total Return =(1+.033)(1-.025)(1+.05)=1+5.753375% Average Return = Annualized Return=

14. 14 Examples of Time-Weighted R of R Use the data for BillyBob and Fred and the Time-weighted (geometric) rate of return. How do your answers compare to the statistical return? Why?

15. 15 Examples of Time-Weighted R of R Things To Do: II-4 William Gates III gives me $1,000,000 to invest. At the end of the first year I must report to Mr. Gates a loss of 50% for the year. However, at the end of the second year I report a gain of 100% for the year. A.What is the market value of Mr. Gates’ portfolio at the end of the two year period? B.What is the average return on Mr. Gates’ portfolio? C.What is the expected annual return on the portfolio in year 3?

16. 16 Returns Using Arithmetic and Geometric Averaging Arithmetic r a = (r 1 + r 2 + r 3 +... r n ) / n r a = (.10 +.25 -.20 +.25) / 4 =.10 or 10% Geometric r g = {[(1+r 1 ) (1+r 2 ).... (1+r n )]} 1/n - 1 r g = {[(1.1) (1.25) (.8) (1.25)]} 1/4 - 1 = (1.5150) 1/4 -1 =.0829 = 8.29%

17. 17 Dollar Weighted Returns Internal Rate of Return (IRR) - the discount rate that results in present value of the future cash flows being equal to the investment amount. Approaches rate of return like a capital budgeting problem in corporate finance. –Considers changes in investment –Initial Investment is an outflow –Ending value is considered as an inflow –Additional investment is a negative flow –Reduced investment is a positive flow

18. 18 Examples-Dollar Weighted Returns You are given a trust of 100,000 to manage. You must pay-out $5,000 at the end of each of the next three years. The trust is terminated at a target value of $110,000 at end of year three. Verify that you must earn a constant return of 8.1% to meet the demands of the trust.

19. 19 Examples-Dollar Weighted Returns What rate of return would be required if the payment were 4,000 and the terminal value of the trust was required to be 110,000? What rate of return would be required if the payments were 3,000 and the terminal value of the trust was required to be 115,000?