Fixed Income PM + Mortgage Hedges - R25/26

Question 1

What is the effect of leverage on return?

Answer 1

R_p = R_i + [(B/E)x(R_i - c)]

R_p =return on portfolio

R_i = return on invested assets

B = amount of leverage

E = amount of equity invested

c = cost of borrowed funds

Question 2

Effect of leverage on duration

Answer 2

D_p = [D_iI - D_BB] ./ E

D_p = duration of portfolio

D_i = duration of invested assets

D_B= duration of borrowings

I = amount of invested funds

B = amount of leverage

E = amount of equity invested

Question 3

Discuss the use of repos to finance bond purchases and the factors that affect the repo rate.

Answer 3

The Repo rate increases as:

• Credit risk of the borrower increases
• Quality of the collateral decreases
  
  • If collateral availability is abundant, repo rate increases (and vice versa)
• Term of the repo increases
• There is no delivery (physical delivery means lowest rate)
• the higher the fed funds rate is
• demand for funds at financial institutions change based on season factors (depends)

Question 4

Critique the use of standard deviation, target semivariance, shortfall risk, and value at risk as measures of fixed-income portfolio risk.

Answer 4

Problems with SD and Variance are:

• Bond returns not often normally distributed
• Number of inputs significantly increases with larger portfolios (difficult to calculate)
• Historically calculated risk measures may not represent the risk measures observed in the future

Problems with Semivariance (dispersion of returns below target)

• Difficult to compute for large portfolio
• If returns are symmetric, semivariance = variance, and variance is better understood.
• If not symmetric, difficult to forecast downside risk and semivariance may not be a good indicator of future risk
• Since only estimated with half the distribution, it is less accurate.

Shortfall Risk (measures the probability the actual return are less than target return) and Value at Risk

• Does not consider the impact of outliers so the magnitude (dollar amount) of the shortfall below the target return is ignored

Question 5

What is dollar duration

Answer 5

Dollar duration is the dollar change in the price of a bond, portfolio or futures contract from a given change in the yield.

For a given bond with an initial value:

(_%_chg value) = -(effective dur.)(decimal chg in int. rates)

Multiplying through by the market value of the bond or portfolio, we get dollar duration, presented by DD:

DD = (_$_chg value) = -(effective dur.)(dec. chg in int rates)(value)

Question 6

Dollar Duration of Futures

How can you find the DD_futures

How can you determine the number of futures contracts to change a portfolio’s dollar duration to a target?

Answer 6

DD_futures = (duration)(decimal ►y)(price) or

DD_futures = DD_CTD/Conversion Factor

contracts = [(DD_target - DD_portfolio)/DD_futures]*(yield beta)

Question 7

Compared to cash market instruments, futures have 3 advantages:

Answer 7

1. Are more liquid.
2. Are less expensive.
3. Make short positions readily attainable (more easily shorted than actual bond)

Question 8

What is basis risk and how can you further define the hedge ratio?

Answer 8

The basis is the difference between the spot price and the futures price.

Basis risk is the variability of the basis, or the risk that the basis will move adversely.

Hedge ratio = exposure of bond to risk factor / exposure of futures to risk factor

Question 9

Determine the hedge ratio to minimize risk in a cross hedge. What is the formula that incorporates yield beta (obtained via regression)?

Answer 9

Question 10

What are the three principal credit-related risks that can be addressed with credit derivative instruments:

Answer 10

1. Default risk
2. Credit spread risk
3. Downgrade risk

Question 11

What are six of the potential sources of excess return on international bonds?

Answer 11

1. Market selection
   
   • Selecting appropriate country markets
2. Currency selection
   
   • To hedge or not to hedge
3. Duration management
   
   • Pick maturities. Maybe use derivatives in less extensive markets
4. Sector selection
   
   • Basically domestic bond portfolio management
5. Credit analysis
   
   • Recognize value-added opportunities
6. Markets outside the benchmark
   
   • Seek opportunities to add value (ie, corps)

Question 12

Interest Rate Parity

What is the arbitrage-free relationship?

What is the approximation of the forward premium or discount?

Answer 12

F = S₀ (1+c_d / 1+c_f)

F and S₀ in DC/FC relationship

We can approximate the forward premium or discount (ie the currency differential as the difference in short-term rates:

f_d,f = (F - S₀) / S₀ is approx = c_d - c_f

Question 13

There are three basic sources of hedging error:

Answer 13

There can be an error in the:

1. Forecast of the basis at the time the hedge is lifted
2. Estimated durations
3. Estimated yield beta

Question 14

What are the 3 techniques to hedge currency risk?

Answer 14

1. Forward hedge - this is used to eliminate most of the currency risk. The manager enters a forward contract to sell the foreign currency at the current forward rate.
2. Proxy hedge - the manage enters into a forward contract between the domestic currency and a second foreign currency that is well correlated with the first foreign currency (ie, using USD as a proxy hedge against a 2nd US-pegged currency)
3. Cross hedge - Contract to deliver the original foreign currency for a third currency.

Question 15

What is the breakeven yield change?

Answer 15

change in price = -duration x breakeven yield change

solving for chg y (where chg y = breakeven yield change)

chg y = change in price/ -duration

ie

chg y = -0.125%/-6.3 = 0.0198 or 1.98 bps

Question 16

What are the criteria that are utilized in determining the optimal mix of active managers?

Answer 16

• Style analysis
• Selection bets
• Investment processes
• Alpha correlations

The process is about the same for selecting equity managers. FI strategies should be low-fee.

Question 17

Explain convexity

Answer 17

Convexity refers to the nonlinear relationship between changes in the value of a fixed income instrument and changes in its yield.

Question 18

Describe the curve of a callable-bond and its impact on convexity

Answer 18

i* in this case is the coupon rate.

Mortgage securities exhibit similar characteristics to the graph, whereas a treasury bond always has positive convexity.

Question 19

What are the 5 risks associated with mortgage securities?

Answer 19

• Spread risk
  
  • Spread between T-bond widening. Focus on OAS
• Interest rate risk
  
  • Different from spread risk, as interest rates can change independently
• Prepayment risk
  
  • cause of negative convexity. This is the reason why an unhedged mortgage security is “market directional”
• Volatility risk
  
  • associated with the prepayment option (a negative). Increased yield volatility = increased option value = decreased value of mortgage security
• Model risk
  
  • Can be from naively projecting past patterns or tech changes which make prepayment more convenient, etc.

Question 20

What is the formula for the covered interest differential?

Answer 20

covered interest differential = (1+c_d)-(1+c_f)(F/S₀)

or

(1+c_d) = (1+c_f)(F/S₀)

Question 21

Describe the process of hedging mortgage securities

Answer 21

In short, the manager wil use two bonds to construct the hedge - one is sensitive to changes in short interest rates and the other to longer interest rates.

1. Given assumed positve/negative change in interest rates, determine the average absolute price change per $100 of the MS and the 2 hedging instruments
2. Given the assumed twist in the yield curve, determine the avg. price change for the mortgage security and each of the two hedging instruments
3. Set up a system of two equations to determine the amount in each hedging instrument
4. Solve for the amounts of the two securities that should be shorted.