qf-core — Quantitative Finance Practice Questions

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1. A portfolio has a daily expected return of 0.05% and a daily volatility of 1.2%. Using the parametric method a
2. If the investor's coefficient of relative risk aversion is γ = 4, what is the Merton optimal fraction (π^*) to
3. Calculate the price of a zero-coupon bond that pays $1000 in two years, given that the one-year discount facto
4. If the risk-neutral probability of an up move is p = 0.6, what is the expected stock price at the end of two s
5. According to the Merton portfolio problem, what is the optimal fraction π^* of wealth to hold in the risky ass
6. If the flat yield curve is at 4% (continuously compounded), what is the bond's price?
7. What is the fair no-arbitrage price for a six-month (T = 0.5) forward contract?
8. If yesterday's return was 2% and the conditional variance was 0.0001, what is the updated conditional volatili
9. According to the Merton optimal portfolio fraction, what percentage of wealth should be in the risky asset?
10. As the number of assets n approaches infinity, what happens to the total portfolio variance?
11. A bond's price P is a function of its yield y. If the second derivative P''(y) is positive, how does the durat
12. What is its Macaulay duration?
13. Calculate the one-year survival probability for a corporate bond with a constant hazard rate of λ = 0.04 per y
14. If the assumed recovery rate in the event of default is 40%, what is the implied annual hazard rate (λ)?
15. What is the fair par swap rate?
16. What is the optimal fraction of wealth to invest in the risky asset?
17. If the risk-free rate is r = 0.05 and the horizon is T = 0.5 years, what is the no-arbitrage forward price F_0
18. If the market assumes a recovery rate of 40%, what is the implied annual hazard rate (default intensity) λ?
19. If the market yield increases from 4.0% to 4.5%, what is the estimated percentage change in the bond price?
20. Given a risk-free rate of 3%, which strategy is superior on a risk-adjusted basis according to the Sharpe Rati
21. A $20 million equity portfolio has an expected daily return of 0.05% and a daily volatility of 1.4%. Assuming
22. If the risk-free rate is r=3%, what is the 'distance to default' d_2 in the Merton model?
23. Using a simple credit spread approximation, what is the implied annual hazard rate λ for a bond trading at a s
24. If a corporate bond has a 5-year cumulative survival probability of 81.87% under a reduced-form model with a c
25. A portfolio worth V = 20 million has an expected daily return of 0.05% and a daily volatility of 1.4%. Calcula
26. In the Merton structural model of credit risk, a firm has assets worth A_0 = 200 million and asset volatility
27. According to the Capital Asset Pricing Model (CAPM), what is the required rate of return for this stock?
28. Using the standard approximation, what is the fair CDS spread s in basis points?
29. A portfolio manager is diversifying a portfolio. If she adds a new asset that is completely 'uncorrelated' (ρ=
30. Under the Girsanov theorem, to transform a process with real-world drift μ into a risk-neutral process with dr