# Interest Rate Risk Management: A Comprehensive Guide for Investors

Classified in Mathematics

Written at on English with a size of 4.73 KB.

## Management of Interest Rate Risk

### Major Risks in Bond Market

**A) Interest Rate Risk** (change in market prices of bonds due to varying interest rates)

- Increase in rates, decrease in market prices, increase in reinvestment rate risk (coupons reinvested at lower return)

**B) Reinvestment Rate Risk** (uncertainty of rate at which interim cash flows can be reinvested)

- High coupon rate, high reinvestment rate risk
- Greater for longer holding periods (high interim cash flows)

**C) Default Risk** (credit risk) (issuer unable/unwilling to pay interest and principal of bond)

- High credit rating, lower yield
- Short-term T-bills (almost risk-free, no default risk, and low return and reinvestment risk because of short duration)

**D) Call Risk** (risk bond issuer will redeem bond before they mature)

-"Call i" if decrease in rates/increase in prices ---"bond refundin" (new bond, lower coupon)

**E) Inflation Risk** (value of cash flows vary with change in purchasing power) (Real return = Nominal return + inflation)

- TIPS protect against inflation (adjust with CPI, fix coupon rate. Face value is $1000, inflation rises 3%, adjusted principal $1030)

**F) Liquidity Risk** (marketability risk) (ease at which bond can be sold at or near value)

- Wider dealer spread, higher liquidity
- Example: 10-year bond/5% annual coupon/at par: YTM=1.05
- P=($50/1.05)+...($1050/1.05^10)
- Rate increase by 5 basis points: 0.05% increase
- YTMP=($50/1.0505)+...($1050/1.0505^10) (increase in yield, decrease in bond price)
- (Long-term bonds have higher exposure to interest rate risk)

### Duration

**A) Macaulay's Duration**

- D=(PV
*CF1)/P+...+(PV*CF)/P*t - Weighted average time until cash flows are received (in years)
- Example: 1-year zero coupon bond
- P=$95.24 => $94.34 (about 1% drop)
- D=1

**B) Modified Duration**

- =Duration/(1+y)
- Price sensitivity with respect to the yield
- Example: Modified duration=12 years. %change in P when yield increases by 10 basis points?
- P changes by -12*0.1% = 1.2%

**C) DV01** - the"price of a basis poin" (1bp = 0.01%)

- =(P*D/(1+y))/10,000
- (-1/10,000) * (dP/dy)
- Positive DV01 bond value is negatively associated with the yield (yield rises 1bp, bond value decreases by DV01)

**D) Duration and Price Change** (APPROXIMATE)

- Change P = -(D/(1+y))
*P*change y - (Change in bond P, with change in rates)
- Example: 10-year par bond/8% annual coupons
- Price change when yield goes up by 5 bp.
- Change P= -(1/1.08)
*duration*$1000*0.05% = -$3.36

**E) Key Rate Duration**

- Measure bond price sensitivity at key point on yield curve
- =(P 1% decrease in yield - P 1% increase in yield)/(2
*0.01*P original)

**F) Duration Properties**

- Inversely related to coupon rate
- Inversely related to yield to maturity
- Increases with time to maturity

**G) Duration of a Bond Portfolio**

- =(P1/P1+P2)
*Dur.1 + (P2/P1+P2)*Dur.2

### Immunisation

-inv. and financial institutions are subject to interest rate risk.- uncertainty in future int. rates lead to P risk and Re. risk

- CF matching (payoff exact required CF)
- Duration matching (matches D of assets and liab.)

ex. flat yield curve, at 6%, bought 100 5-year, 4% coupon bond, FV = $10001.- P= ($40/0.06)*(1-1/1.06^5)+$1000/1.06^5 = $915.75- duration= 4.611 years, duration 10-year zero= 10years- P= -D/D hedge * P- Mkt Value= 100*915.75 = $ 91,575