Finance 00 Financial Markets Lecture Fall, 2001

Finance 300 Financial Markets

• Lecture 2

• Fall, 2001©

• Professor J. Petry

• http://www.cba.uiuc.edu/broker/fin300/fin300pp.htm

Chapter II-Portfolio Theory

• 1. Measuring Portfolio Risk & Return

• 2. Diversification

• 3. Capital Asset Pricing Model (CAPM)

• 4. Arbitrage Pricing Theory (APT)

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)

Holding Period Rate of Return

Examples

• HPR with V0 of 1,000,000 and V1 of 1,300,000

• R = 1,300,000/1,000,000 = 1.30 = 1 + 30%

• HPR with V0 of 200,000 and V1 of 134,000

• R = 134,000/200,000 = 0.67 = 1 - 33%

• HPR with V0 of 2,000,000 and V1 of:

• 2,124,770 HPR =

• 1,843,748 HPR =

• 2,000,000 HPR =

Cash Flow Adjusted Rate of Return

Examples

• HPR of 1 month investment with V0 of 2,000,000 and V1 of 2,575,000. R = 1 + 28.75%

• And if 500,000 was invested on the last day of the month?

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?

Cash Flow Adjusted Rate of Return

Cash Flow Adjusted Rate of Return

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.

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?

Time-Weighted Rate of Return

Examples of Time-Weighted R of R

Returns Using Arithmetic and Geometric Averaging

• Arithmetic

• ra = (r1 + r2 + r3 + ... rn) / n

• ra = (.10 + .25 - .20 + .25) / 4

• = .10 or 10%

• Geometric

• rg = {[(1+r1) (1+r2) .... (1+rn)]} 1/n - 1

• rg = {[(1.1) (1.25) (.8) (1.25)]} 1/4 - 1

• = (1.5150) 1/4 -1 = .0829 = 8.29%

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

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.

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?