FFM Final Exam Review

1. FFM Final Exam Review

2. Final exam general info • 50% of your final grade • 12 multiple choice (4 pts each) – 48% • 6 open-ended (varying points) – 52% • Allowed two double-sided page of notes

3. Studying strategy • You have to know time value of money • Draw time lines if you get confused • Review CAPM theory • Go over homework and additional practice problems covering concepts from the second half of class • Don’t worry about making the Ultimate Cheat Sheets, it’s a waste of time

4. Time value of money • PV vs. FV • In general: FV=PV(1+r)^t • Compounding • N times a year: FV=PV(1+r/N)^(Nt) • Continuous compounding: FV=PVe^(rt)

5. Annuities and perpetuities • Formulas assume first payment C starts one period in the future

6. Portfolio with two securities There can be a negative weight (shorting) = variance = volatility/standard deviation

7. Risk-free security • Expected return is the same as realized return, always, meaning that the variance and standard deviation are zero.

8. CAPM • Portfolio theory and the tangency portfolio • CAPM: tangency portfolio = market portfolio • What is the market portfolio? • If CAPM holds, how do investors behave?

9. CAPM Risk: diversifiable vs. un-diversifiable β (beta) measure of un-diversifiable risk E[ri] determined by βi, always

10. Valuation • In this class, you valued companies’ equity based on the idea that a stock is worth the present value of its future cash flows. • What was the appropriate discount rate?

11. Dividend discount model

12. Constant dividends

13. Growing dividends

14. Calculating growth rate

15. Valuation example • Using the following information, value the equity of the following company: • β=1.5, rf=5%, rm=10% • D1=$10, D2=$8, D3-D∞=$14

16. Solution • k= rf + β(rm-rf) = 12.5%

17. Fixed income: Bond concepts A bond is an agreement between the issuer of the bond and the holder The issuer receives the money upfront and then pays it back over time The holder pays money upfront and receives it back over time Buying a bond is lending Shorting a bond is borrowing

18. Basic characteristics of bonds Principal (same as “face value”) Maturity (time until principal repaid) Coupons (periodic payments until maturity) Yield (the return offered by the bond)

19. Pricing bonds Present value (discounting by the bond’s yield) of all cash flows: Using annuity formula for coupons:

20. Inverse price/yield relationship Remember that the yield is the discount rate, and the higher the discount rate, the lower the present value. Intuitively, if investors demand a greater return (greater yield), they will pay a lower price for given future cash flows.

21. Example Bond with following characteristics: Principal: $1,000,000 Maturity: 10 years Coupon rate: 10% (annual payments) Yield: 5% Discount, par, or premium bond? Price?

22. Solution (Premium bond)

23. Yield to maturity • YTM is only realized if: • Bond held to maturity (why?) • Coupons reinvested at same rate (why?)

24. Duration risk • Duration risk is interest rate risk that arises from not holding a bond to maturity

25. Duration risk example • Suppose you bought a $1000 face value three year zero-coupon bond with y=4% and sold it two years later (one year before maturity) • If, at maturity, the yield is still 4%, what was your holding period return? • If instead the yield rose to 6%, what was your holding period return?

26. Solution • Price of bond when you bought it was: • If yield remained 4%, selling price was: • If yield rose to 6%, selling price was:

27. Solution (cont.) • Therefore, if yield remained 4%, HPR was: • If yield rose to 6%, HPR was:

28. Forward rates Future yields implied by “spot” yields Expectations theory f1 f2 f3 f4 t=0 1 2 3 4 y1 y2 y3 y4

29. f1 f2 f3 f4 t=0 1 2 3 4 y1 y2 y3 y4

30. Options • Call vs. put: • Call option: right to buy underlying security • Put option: right to sell underlying security • Characteristics: • Exercise type (American vs. European) • Strike price • Expiration

31. Option payoffs and profit • Call: • If ST>X, exercise (buy stock for X) • If ST<X, do not exercise (option worthless) • Therefore, call payoff is max[ST-X,0] • Put: • If ST>X, do not exercise (option worthless) • If ST<X, exercise (sell stock for X) • Therefore, put payoff is max[0,X-ST]

32. Example: call fly • S0=100 • Buy call with X=90 for $22 • Sell two calls with X=100 for $15 • Buy call with X=110 for $13 What is the cost of this call fly? If ST=105, what is your payoff and profit?

33. Solution • Payoff for X=90 call: max[105-90,0]=$15 • Payoff for X=100 calls: max[105-100,0]=$5 • Payoff for X=110 call: max[105-110,0]=0 • Total payoff: 15-2*5+0=$5 • Profit=payoff-cost=5-5=0

34. Put-call parity • Suppose you buy a call and sell a put with identical strike prices • What happens when ST>X? Buy stock for X. • What happens when ST<X? Buy stock for X. • Thus, being long a call and short a put at the same strike is the same thing as agreeing to buy a stock in the future for X.

35. Put-call parity

36. Binomial pricing model • Given two possible stock prices in the future and a risk-free interest rate, we can construct an arbitrage-free portfolio that replicates the payoff of a stock option. • Portfolio will consist of long/short position in the stock along with a short/long position in the risk-free security