There is a bond, which has a duration of 7 and a convexity of 40. Compute exact and approximate prices. a) If the bond increases by 3 %, what will its price alter by? b) If it decreases by 3%, what will the alteration of price be? c) Discuss without derivations. Are the true results symmetric in the 2 cases? How do I find the price using the present value of the future cash flows?

There is a bond, which has a duration of 7 and a convexity of 40. Compute exact and approximate prices. a) If the bond increases by 3 %, what will its price alter by? b) If it decreases by 3%, what will the alteration of price be? c) Discuss without derivations. Are the true results symmetric in the 2 cases? How do I find the price using the present value of the future cash flows?

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Suppose that x is the continuously compounded yield to maturity on a zero-coupon bond that pays off $1 at time T. Assume that x follows the process: dx = a (x₁ - x) dt + sx dz where a, x0, and s are positive constants and dz is a Wiener process. What is the process followed by the bond price? Solutions:
Do solve all parts A. What risk premium do you use? Why? B. Why is the geometric mean lower than the arithmetic mean for both bonds and bills? C. If you had to use a risk premium with the longer periods, what biases will the investor have?
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Suppose an investor observes an upward term structure of interest rate. Answer the followingquestions. (a) According to the expectation hypothesis, what will be the investor’s forecast about futurechange of interest rate (increase, decrease or unchanged)? (b) What will the investor say about the future change of interest rate according to liquiditypreference theory? Explain your argument.
Which of the following investments will experience the largest change in its market value as a result of changes in the level of interest rates (we are talking about the absolute value of the change, up or down)? Suppose interest rates go up or down by 50 basis points (0.5%). Rank the investments from 1 to 4 where a 1 is the most affected (largest absolute change in value) while a 4 is the least affected (smallest absolute change in value). A: $1 million invested in 3-month Treasury bills. 请选择~ B: $1 million invested in STRIPS (zero coupons) maturing in three years. |请选择 C: $1 million invested in a Treasury note maturing in three years. The note pays a 5% annual coupon. |请选择︾ D: $1 million invested in a Treasury note maturing in three years. The note pays a 10.0% annual coupon. |请选择

Assuming two risk-free rates for lending and borrowing in the market: r(f) and r(b). Suppose your utility function is described by U = E(r) - 0.5A xo² with A> 0, and you are combining the risk-free asset with the optimal risky asset to maximize the utility. Consider the following two situations: 1. Suppose r(b) = r(f): you form the optimal complete portfolio C1 by borrowing money at r(f) and invest y1 (i.e., y1 represents portfolio weight) in the optimal risky portfolio (P1). Your utility score under this situation is denoted as U1; II. Suppose r(b) >r(f): you form another optimal complete portfolio C2 by borrowing money at r(b) and invest y2 (1.e., y2 represents portfolio weight) in the optimal risky portfolio (P2). Your utility score under this situation is denoted as U2. For simplicity, let's assume the optimal risky portfolios under these two situations are the same (i.e., E(P1)=E(P2) and o(P1) = o(P2)). What are the relationship between y1 and y2, U1 and U2: O a. y1=y2 and U1=U2 O…
An efficient capital market is best defined as a market in which security prices reflect which one of the following? Multiple Choice A Current inflation B A risk premium C All available information D The historical arithmetic rate of return E The historical geometric rate of return
Derive the inverse relationship between Price and Yield in debt markets using a property-based example where the market price doubles in value but ultimately falls by one third of the initial price and where the initial rental yield is 6%. Include an explanation or commentary along with your calculations and proof.
Consider a capital market with two securities. The payoffs of these securities in the two equally likely states of the world are given in the table below. Рayolf Price Security State 1 State 2 PA=2 A 4 2 PB-3 B a. Discuss the concepts of complete capital markets, pure (Arrow-Debreu) securities, and pure factor portfolios. Establish whether the capital market in this case is complete and determine the prices of the pure socurities by arbitrage.
D3) Finance Consider an option with α being a non-negative parameter and the option pays ((S(T))α − K)+ at maturity date T. Let Cα(S(0), σ, r) be the risk neutral price of the option (with interest rate r and volatility σ) when the initial price is S(0). Obviously, C1(S(0), σ, r) = C(S(0), σ, r) is the price of an ordinary call option. Show that, Cα(S(0), σ, r) = e(α−1)(r+ασ2/2)TC((S(0))α, ασ, rα), where rα = α(r − σ2/2) + α2σ2/2.

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