Quiz5-7_Solutions (1)

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QUIZ 1 - Q1 (1+rA) = e^(rc) rA 6.00% rc 5.83% QUIZ 1 - Q2 rt: P= F/((1+rt)^t) F1 1000 F2 1000 P1 934.58 P2 811.62 t 1 t 2 r1 7.00% r1 11.00% QUIZ 1 - Q3 An interest rate is 6% per annum with annual compounding. What is the equivalent rate with continuous compounding? You know a 1-year zero-coupon bond with a face value of $1000 has a price of 934.58. You also know a 2-year zero-coupon bond with a face value of $1000 has a price of 811.62. What are the 1- year and 2-year spot rates (denoted by r1 and r2, respectively) in this economy? What does the "term structure of interest rates" tell you? Limit your answer to around 100 words (or less). The term structure of interest rates (or yield curve) tells us the relationship between the spot rates in the economy and different maturities. In normal times, spot rates increase with maturities. An inverted yield curve occurs when investors believe that a recession is coming.

QUIZ 2 - Q1 0 1 2 3 Spot rates (rt) 3.29% 3.90% 4.20% Discount Factors 0.96812 0.92633 0.88388 Bond A CFs 150 150 1150 Discounted CFs 145.22 138.95 1016.46 PV(CFs) 1300.63 Price 1300.63 Goal Bond A 0.000 Bond B CFs 60 60 1060 Discounted CFs 58.09 55.58 936.91 PV(CFs) 1050.58 Price 1050.58 Goal Bond B 0.000 Bond C CFs 100 1100 0 Discounted CFs 96.81 1018.97 0.00 PV(CFs) 1115.78 Price 1115.78 Goal Bond C 0.000 QUIZ 2 - Q2 time 0 1 2 3 4 5 cash flow 100 20 0 0 12 -0.5 False, because one of the cashflows is strictly negative. What is the term structure of interest rates (r1, r2, r3), given the following bonds? (A) a 3-year coupon bond with face value of $1000 and annual coupon rate of 15%, currently trade (B) a 3-year coupon bond with face value of $1000 and annual coupon rate of 6%, currently traded (C) a 2-year coupon bond with face value of $1000 and annual coupon rate of 10%, currently trade The following cashflows are associated with an arbitrage strategy. True or False?

QUIZ 2 - Q3 time 1 2 3 4 future cash flows 30 35 40 50 0 1 2 3 4 Spot rates (rt) 5.00% 7.00% 8.00% 8.80% Discount Factors 0.95238 0.87344 0.79383 0.71365 CFs 30 35 40 50 Discounted CFs 28.57 30.57 31.75 35.68 PV(CFs) 126.58 Given the traded bonds in the economy, the spot rates are: r1=5%, r2=7%, r3=8%, r4=8.8%. You encounter an asset that is currently traded at $120 and gives you the following future cash flow (A) a 3-year coupon bond with face value of $1000 and annual coupon rate of 15%, currently trade Is there an arbitrage opportunity in the market? If there is one, what is the arbitrage profit that you can generate today? Yes, there is an arbitrag opportunity because the present value of the cashflows $126.58 (obtained the economy) is not equal to th eprice oif the asset $120. In particular, the asset is undervalued. Th to the mispricing $126.58 - $120 = $6.58 (or 6.6 with only one decimal)

ed at $1300.63 d at $1050.58 ed at $1115.78

ws: ed at $1300.63 d using the spot rates in he arbitrage profit is equal

QUIZ 3 - Q1 C 4.31 K 50 ST 56.00 52.00 37.00 Call Payoff 6.00 2.00 0.00 Call Profit 1.69 -2.31 -4.31 QUIZ 3 - Q2 Bid Ask P1 9.25 9.3 K1 130 P2 2.05 2.1 K2 100 ST 140.00 105.00 80.00 Put 1 Payoff 0.00 25.00 50.00 Put 2 Payoff 0.00 0.00 20.00 Potfolio Profit -7.25 17.75 22.75 =B31-B32-($C$25-$B$27) QUIZ 3 - Q3 The stock of Pfizer is currently trading for $45, and you consider buying a call option written on of $50 and expiration in one year. The call option costs $4.31. What will be your profit if Pfizer's stock price in one year is $56, $52, or $37? The stock of Moderna is currently trading for $132, and you consider buying a put option writte strike price of $130 and expiration in one year, and at the same time selling a put option written price of $100 and expiration in one year. The put with a strike of $130 is trading for $9.25-9.30 ( with a strike of $100 is trading for $2.05-2.10 (bid-ask prices). What will be your profit if Moderna's stock price in one year is $140, $105, or $80? AAPL (the stock of Apple) is currently trading for $174.21. A call option written on AAPL with a s expiration date November 18 is trading for $21.85-22.15 (bid-ask prices). A call option written o of $170 and expiration date November 18 is trading for $10.20-10.30 (bid-ask prices). A call opti a strike price of $185 and expiration date November 18 is trading for $2.98-3.00 (bid-ask prices) options in your portfolio, you construct a Butterfly Spread. What is the cost today of building your portfolio (the cost of the Butterfly Spread)? If AAPL price 18, what is the payoff of your portfolio? What is the profit? What is the return?

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