Given a sample size of 252, the annualized volatility (based on daily return) is 20% and the stock price is at $100.
a) What should be the daily VaR for the security given a confidence level of 99%?
b) What is the 95% confidence level of the daily VaR?
c) If there are 5 losses falling outside of the VaR, then the estimation for the VaR is too conservative. Do you agree? Why?
Question 2:
a) Given the following information, what should be the quotes for AMZN 3-month futures? (Assume the interest rates are periodically compounded.)
Bid Ask
AMZN: 808.35 808.55
US 3-month Libor = 0.40% 0.80%
b) If the current futures quotes for AMZN are 808.75 (bid) and 808.90 (ask), could you find any arbitrage opportunities? Please explain.
c) If so, how will you conduct the arbitrage? What are your arbitrage profits?
Question 3:
a) Given the following information, what should be the quotes for USD/JPY 3-month forward rates? (Assume the interest rates are periodically compounded.)
Bid Ask
Spot rate USD/JPY: 104.35 104.45
JPY 3-month Libor = 0.25% 0.75%
US 3-month Libor = 0.40% 0.80%
b) If the current forward rate quotes for USD/JPY are 103.95 (bid) and 104.00 (ask), could you find any arbitrage opportunities? Please explain.
c) If so, how will you conduct the arbitrage? What are your arbitrage profits?
Question 4:
Given the following SPY options prices, could you find any arbitrage opportunities if there is no dividend? If so, please construct the arbitrage procedure and calculate the arbitrage profits.
Time to maturity:
|
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3 months
|
|
3-month interest rate:
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0.10%
|
|
|
Strike
|
Bid
|
Ask
|
Call
|
190
|
6
|
6.1
|
put
|
190
|
6.08
|
6.21
|
SPY spot price:
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190.52
|
190.55
|
Question 5:
Some investors believe the VIX index follows mean-reversion pattern. Do you agree? Why?
(Suggestion: use VIX daily returns from 01/01/2000 ~ present to verify your answer.)
Question 6:
Please depict the return distributions for a) Hedgers, b) Speculators, and c) Arbitragers.
Question 7:
1) Does yield curve predict the equity value in the future?
(https://stockcharts.com/freecharts/yieldcurve.php)
2) Please use a scientific approach to verify your answer in 1).
(Suggestion: use monthly data for yield curve and SPY to conduct a Granger-causality test)