Part 1

True or False (6pts).   Evaluate whether the following statements are true of false.

1. 2pts (True / False) When the yield curve is upward sloping then par curve lies below the forward curve.

Solution. This is true.

2. 2pts (True / False) A portfolio that is key duration (2y, 5y, and 10y) hedged is also duration hedged.

Solution. True.  Jointly 2y, 5y, and 10y shift move the yield curve in parallel.  Hence key rate duration hedged portfolio should not be affected by a small parallel shifts of

the yield curve, i.e., it is duration hedged.

3. 2pts (True / False) A portfolio that is key duration (2y, 5y, and 10y) hedged is also approximately factor hedged (level, slope, curvature).

Solution. True.  A combination of key rate shifts can replicate the level, slope, and curvature shifts of the yield curve.   Hence key rate hedging and factor hedging is effectively the same.

4. 2pts (True / False) A factor hedged hedged (level, slope, curvature) portfolio is also approximately duration and convexity hedged.

Solution. False.  Factor hedged portfolio is duration hedged, but it is not immune to large shifts of the yield curve (so it is not convexity hedged).                                  

5. 2pts (True / False) Evaluating built-in options is important for pricing of the modern MBS.

Solution. True. Prepayment risk stemming from the option of the homeowner to pre- pay the mortgage is the one of the most important factors for pricing MBS securities.

Multiple Choice (6pts).   Answer the following multiple choice questions. Explain your choice in a few sentences.  You will receive 50% of the points for the correct answer and 50% points for the correct explanation.

1. 2pts Suppose you want to value a portfolio with linear fixed and floating payments. Instead of constructing a replicating portfolio out of FRNs and ZCBs you simply replace all floating rates with forward rates and compute the price of this modified portfolio. This method will result in a price:

(a) That is higher than the price of the original portfolio

(b) That is the same as the price of the original portfolio

(c) That is lower than the price of the original portfolio

Solution. The price will be the same since you are simply adding or subtracting FRAs

from the original

portfolio.

2. 2pts Consider a modified inverse floater with annual payments that instead of paying coupon 10% − T1 (T − 1,T) that depends on future spot rates T1 (T − 1,T) it pays a coupon 10% − f1 (0,T − 1,T) that depends on todays forward rates.  Such modified inverse floater will have a duration that is:

(a) Higher that the original inverse floater

(b) The same as the original inverse floater

(c) Lower that the original inverse floater

Explain

Solution. Duration will be lower. To make this transformation, you effectively need to

buy FRAs. Buying FRAs lowers the duration of a portfolio.

3. 2pts Suppose that you have just bought a 6-12mo FRA linked to the Treasury yield curve.  That is the fixed rate in the contract is the 6-12mo forward rate from the Treasury yield curve and the floating rate is the future 6mo spot rate from the Treasury yield curve. What would happen to the price of this FRA tomorrow if the curvature of the yield curve goes up but the level and the slope remain the same? Explain.

(a) The price goes up

(b) The price goes down

(c) The price does not change

Solution. The price would go up.  FRA is effectively long a 6mo ZCB and short 1y ZCB of the same market prices. When the curvature of the yield curve goes up the 6mo rate goes down and the 1y rate goes up. Hence, the long part of the FRA increases in value (6mo rate goes down) and the short part of the FRA decreases in value (1y rate goes up). More assets and fewer liabilities means that the portfolio is more valuable.

4. 2pts Buying swaps

(a) increases the duration of your portfolio

(b) does not change the duration of your portfolio

(c) decreases the duration of your portfolio

Explain why.

Solution. Decreases the duration of your portfolio. A swap is a long position in FRN and short position in a fixed coupon bond. Since FRN has a short duration and FCB has a long duration, the swap is borrowing long and investing short. This lowers the duration of the original portfolio.

Short Answer (6pts).   Answer the following questions.

1. 2pts Why hedging both duration and convexity with a single security, even if such a perfect security exists, is not a good idea?

Solution. The problem arizes from the dynamic nature of hedging.  The security the hedges both duration and convexity today is likely not going to work in a few month. To maintain the hedge one would need to liquidate the whole hedging position and reacquire the new one. This results in large transaction costs.

2. 2pts Explain in your own words why in the March of 2020 the Fed opened the Money Market Mutual Fund Liquidity Facility.

Solution. In March of 2020 investors were withdrawing money from the money market mutual funds. Large withdrawals meant that the mutual fund industry cash reserves were running out and they would have to either sell a large fraction of their assets (short-term debt of non-financial firms) or simply stop rolling the debt over.  At the same time the non-financial firms did not have any revenues due to lockdowns that stopped economic activity, so many of them would not be able to their short term debt if it was not rolled over.  By lending to the mutual funds the Fed stopped this downward spiral: the mutual funds used the money their borrow from the fed to meet their withdrawals without having to liquidate their portfolios, and the non-financial firms were able to keep rolling over their debt without defaulting.                           

3. 2pts Evaluate the following statement:  “The 10y spot rate on March 3, 2022, is lower that the 2y spot rate - which means that the market expects the Fed to lower the target in the future”. Is this statement correct or wrong? Explain.

Solution. This statement is true. Long rates are determined by the market expectations and the risk-premium.  Risk premium is always higher for the longer maturity rates. So with constant expectations the yield curve is upward sloping.  Downward sloping yield curve is a string signal of an expected decrease in the future short rates.