This section gives a detailed implementation of our hedging algorithm. Security to be hedged: MBS
Hedging Instruments: Portfolio of {MBS, Treasury bonds with different maturities} Hedging Method: Dynamic hedging using PCA duration. vs. Conventional duration and convexity hedging
Hedging Parameters: PCA duration
Hedging Error: The net present value of the portfolio, which has initial value of zero Hedging Efficiency: Reduce hedging Error
Hedging Strategy: Construct a portfolio, consisting of MBS and various T-notes, bonds, with 0 face value. Duration matched to 0. Rebalance at each time period to match the hedging parameters; compare the results with duration and convexity hedging. There are two issues we need to pay special attention to, in order to effectively execute the hedging strategy.
Issue 1: With the coupon payment and prepayment of MBS, what needs to be done with this extra cash flow?
Answer: Use this cash flow to rebalance the portfolio, basically to change the weights of Treasury bonds holdings. If the position is short in MBS, and long in Treasury bonds, we need to sell the Treasury bonds to honor the MBS payment.
Issue 2: Some Treasury bonds used to hedging the MBS will expire before the MBS maturity date. This will hurt the capacity of available hedging instruments.
Answer: We only hedge the MBS for a short period of time, e.g. 3 years, and then we can use Treasury bonds with greater or equal to 3 years maturities. Another solution is to introduce on extra hedging instrument when there is one expiring at that period. Hedging Framework
1. |
Get mortgage information; |
2. |
Get historical yield curve data; |
3. |
Get Principal Components Factors; |
4. |
Start clock for hedging period: m=0 |
5. |
Calculate MBS_Price(m), MBS_Duration(m)4xi, Payment(m), |
PrincipalPayment(m); |
Treas _ price(m)' W(m -1) - MBS _ payment(m -1) MBS _ Duration(m)
9. Calculate hedging error:
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