I have some questions about Q19.

It uses the table from Q18.

And i have also attached solutions for Q19.

What i dont get is Q19-b

why is Time 3s cash flow (+) $1,000 and not (-) $ 1,000?

and also Time 5s cash flow is (-) $ 1,204,50 . How did this come about?

I have no idea.

Could you explain in detail?

I have little background knowledge in Finace but i have to take test soon.

So i need really detailed explanation for the questions I have.

And also what is a synthetic two-year mentioned in this Q 19?

18. Suppose that the prices of zero-coupon bonds with various maturities are given in the follmi table. The face value of each bond is $1,000. Maturity (Years) Price $925.93 853.39 782.92 715.00 650.00 2 4 Timerest oy llt Ur for each could you construct a 1-year forward loan beginning in year 3? Confirm that the rate on that loan equals the forward rate. year. . Repeat (b) for a l-year forward loan beginning in year 4. ue to use the data in the preceding problem. Suppose that you want to construct a 2-year aturity forward loan commencing in 3 years. 1 9. Contin a. Suppose that you buy today one 3-year maturity zero-coupon bond. How many 5-year matu- rity zeros would you have to sell to make your initial cash flow equal to zero? b. What are the cash flows on this strategy in each year? c. What is the effective 2-year interest rate on the effective 3-year-ahead forward loan? d. Confirm that the effective 2-year interest rate equals (1 + f) X (1 +fs) -1.You therefore can interpret the 2-year loan rate as a 2-year forward rate for the last 2 years. Alternatively. show that the effective 2-year forward rate equals Similarly, the expected prices of zeros one year from now can be used to calculate the expected bond value at that time: Expected price 1 year from now (S120 0.89278) + (S1,120 0.78293) $107.1336+ $876.8816 $984.02 Total expected rate of returm S120+ ($984.02-$1,003.68) $1,003.68 19. a For each three-year zero you buy today, issue: $782.92/5650.00-1.2045 five-year zeros The time-0 cash flow equals zero. Your cash flows are thus as follows: Time Cash Flow b. S 0 3 $1,000.00 The 3-year zero purchased at time 0 matures; receive $1,000 face value 5 S1,204.50 The 5-year zeros issued at time 0 mature; This is a synthetic two-year loan originating at time 3. The effective two-year interest rate on the forward loan is: issuer pays face value c. $1,204.50/S 1,000-1-0.2045-20.45% The one-year forward rates for years 4 and 5 are 9.5% and 10%, respectively Notice that d. 095x1.10-1.2045 1 + (two-year forward rate on the 3-year ahead forward loan) The 5-year YTM is 9.0%. The 3-year YTM is 8.5%. Therefore, another way to derive the 2-year forward rate for a loan starting at time 3 is: r,(2)-(1+y:1-1.0w -|-0.20462 20.46% [Note: slight discrepancies here from rounding errors in YTM calculations) 15-3 CHAPTER 15