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Class Business

Class Business. Groups Upcoming Homework Stock-Trak Accounts. Returns. How can we compare investment results? Suppose you invest $100 in asset A $95 in asset B At the end of the year, your investment in A has grown to $101 B has grown to $101

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Class Business

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  1. Class Business • Groups • Upcoming Homework • Stock-Trak Accounts

  2. Returns • How can we compare investment results? • Suppose you invest • $100 in asset A • $95 in asset B • At the end of the year, your investment in • A has grown to $101 • B has grown to $101 • So would you be indifferent between these two investments?

  3. Returns • Returns are the correct measuring stick to compare investments. • Gross return: • A: 101/100 = 1.01 = 101% • B: 101/95 = 1.06 = 106% • In general: GRt+1=Gett+1/Payt • GRt+1=the gross return realized at time t+1 • Gett+1=the amount of money you get at time t+1 • Payt = the amount of money you invested at time t

  4. Returns • Net return: • A: 101/100 --1 = 0.01 = 1% • B: 101/95 – 1 = 0.06 = 6% • In general: NRt+1=Gett+1/ Payt - 1 • NRt+1=the net return realized at time t+1 • Gett+1=the amount of money you get at time t+1 • Payt = the amount of money you invested at time t • Note: net return = gross return – 1 • In general when I say “return” I mean the net return.

  5. Returns: Example • Suppose you pay $30 in some investment and get back $33. • What is the gross return? • GR=33/30=110% • What is the net return? • NR = 1.10 - 1 =10%

  6. Returns to a Portfolio • Suppose you invest $10,000 in 3 stocks. • 1:GE 2: NKE 3: OMX • How much do you put in each? • Suppose you divide money accordingly: • GE: 2,000 NKE: 5,000 OMX: 3,000 • Suppose over a period, returns are: • r1=10%, r2=5%, r3=-5% • What is the return on your portfolio?

  7. Net Returns to a Portfolio • Net return: • So the net return on the portfolio is just the weighted average of the net returns of the individual assets in the portfolio • Weights are the fraction of investment in each asset • This works no matter what your initial investment is, or how much you put in each asset. • This extends to gross return

  8. Returns to a Portfolio: Example • Suppose your investment equity is $1000 • 30% is in IBM • 10% is in Microsoft • 60% is in Dell • rIBM=8%, rMSFT=10%, rDELL=-5% • What is the return on your portfolio? • rp=.30(0.08)+0.10(0.10)+0.60(-0.05) • =0.40%

  9. Time Value of Money • Why are asset returns on average positive? • Time value of money • Would you rather have a car now or wait five years? • Present values are not equal to future values

  10. Future Value • Suppose the interest rate is 10%. • If you invest $100 now, • How much do you have in 1 year? • How much do you have in two years? • How much do you have in three years? • In general: Sn=P0(1+r)n • Sn= the value you have at the end of year n • P0= initial principal invested • r = return on investment • n = number of time periods

  11. Present Value • Suppose you can borrow and lend at 10% • Suppose you are offered • $100 in 10 years • $X now • What amount of cash (X) would make you indifferent between the two deals? • X = 100/(1.1010) = $38.55 • In general: PV(Sn)=Sn/(1+r)n • Sn= the value you will receive at the end of year n • r = return associated with risk of receiving Sn • n = number of time periods until money is received

  12. Example: Present and Future Values • Suppose you invest $100 now, and earn a return of 7% every year for 50 years. How much do you have at the end of the 50 years? • Sn=100(1.07)50 = 2945.70 • What is the present value of 1 million received in 50 years if you can borrow and lend at 7%? • PV($1M)=$1M/(1.07)50 = 33,947.76

  13. Effective Rate of Return • Rates of return are time specific. • The effective rate is the actual rate earned over an alternative time period • Example: • 6-month rate is 5% • What is effective annual rate? • First six months: • Each dollar invested grows to 1.05 • Next six months: • Each dollar invested grows to (1.05)(1.05)=(1.05)2 • Effective net annual rate is (1.05)2-1 = 10.25%

  14. Effective Rates of Return • In general, effective rates satisfy the following equation: (1+rA)n=(1+rB) Where • rA is the effective A-period rate (e.g. a month) • rB is the effective B-period rate (e.g. a year) • n is the number of A time periods in B (e.g. 12)

  15. Example - Effective Rate • The annual rate is 15% • What is effective 1-month rate? • Invest $1 • In one year you have 1.15 • Invest $1 at 1-month rate rm • In one year you have (1+ rm)12 • (1+ rm)12 = 1.15, solve for rm • rm = 1.012% • 1.2% monthly return

  16. Annual Percentage Rates (APR) • Example: • Suppose 1-month rate is 1% • APR=12 x .01=12% • Example: • Suppose 1-week rate is 0.3% • APR=52 x .003 = 15.6% • APR is found by multiplying rate by number of time periods there are in 1 year.

  17. Example: Effective Rates & APR • Suppose the current 4 month rate is 3%. • What is the effective annual rate? • (1.03)3=1.0927 • Effective annual rate is 9.27% • What is the APR? • APR=.03 x 3 = .09

  18. Characterizing Risk • We can construct returns, now we introduce uncertainty about possible outcomes and how to integrate this notion into investment characterization and evaluation • Use Probability models from Statistics

  19. Probability Models • Think about flipping a coin. • Only two possible outcomes: • Heads • Tails • Suppose if heads is flipped, we get $1 • If tails is flipped, we win $0.80

  20. Probability Models • What do we expect to get on average? • Game: The coin is flipped 100 times. • What would be your forecast of the payoff from playing this game? • How much would you pay to play this game (price)?

  21. Probability Models • Suppose price to play = $0.85 • We can draw a model of net returns: • Two-state probability model • Two states • Two returns • Two probabilities

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