FINA 469 Lecture Notes - Lecture 9: Feta, Ath, Firn
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Consider a stock currently worth $80 (S = 80) that can go up or down by 25 percent per period. The exercise price is $80 (X = $80) and the risk-free rate is 5 percent (r = .05). The option will expire at the end of the third period (t = 3). You try to find a theoretically fair value of the put option using a three-period binomial option pricing model. Answer the following questions.
t = 0 | t = 1 | t = 2 | ||
Suu = (c) | ||||
Su = (a) | ||||
S = $80 | Sud = (d) | |||
Sd = (b) | ||||
Sdd = (e) | ||||
Puu = (f) | ||||
Pu = (i) | ||||
P = (k) | Pud = (g) | |||
Pd = (j) | ||||
Pdd = (h) | ||||
a) What are three possible stock prices at time t = 2 (c, d, and e)?
b) Compute three values at time t = 2 of European put options. (Puu, Pud, and Pdd)
c) Compute two values at time t = 1 of a European put options (Pu and Pd).
d) Find the theoretical fair value of the put option today (P).
e) Compute the riskless hedge ratio (h).
f) Construct a riskless hedge position with stocks and 1,000 put options at the theoretically fair value using the riskless hedge ratio (h).
Sector | Portfolio Weighting | (2) S&P Weighting | (3) Differences in Weighting | (4) Portfolio Return | (5) S&P Return | (6) Sector Over- or Under Performance | (7) = (3) x (6) Sector AllocationContributions |
Telecommunications Services | 3.10% | 5.90% | A. (2.80%) | 2.50% | 3.10% | K. (-0.60%) | U. (-1.68%) |
Utilities | 7.50% | 3.80% | B. 3.70% | 3.10% | 1.90% | L. 1.20% | V. 4.44% |
Information Technology | 14.30% | 17.90% | C. (-3.60%) | 4.90% | 3.20% | M. 1.70% | W. (6.12%) |
Materials | 6.30% | 3.70% | D. 2.60% | 4.80% | 5.10% | N. (-0.50%) | X. (1.30%) |
Financials | 13.40% | 17.10% | E. (-3.70%) | 6.20% | 4.80% | O. 1.40% | Y. (5.18%) |
Consumer Discretionary | 12.70% | 13.50% | F. (-0.80%) | 2.10% | 4.00% | P. (-1.90%) | Z. 1.52% |
Industrials | 14.10% | 11.90% | G. 2.20% | 4.90% | 3.10% | Q. 1.80% | AA. 3.96% |
Energy | 8.40% | 8.00% | H. 0.40% | 3.70% | 8.60% | R. (-4.90%) | BB. (-1.96%) |
Healthcare | 15.30% | 11.70% | I. 3.60% | 9.80% | 5.70% | S. 4.10% | CC. 14.76% |
Consumer Staples | 4.90% | 6.50% | J. (-1.60%) | 1.50% | 13.20% | T. (-11.70%) | DD. 18.72% |
4. Which sector made the greatest negative contributionto the portfolioâs performance? Explain why this investment madethe greatest negative contribution based on the differences inweighting and the sector over- or under- performance.