# 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=(PVCF1)/P+...+(PVCF)/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))Pchange 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)/(20.01P 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

- shield from interest rate fluctuation. ex:
1. CF matching (payoff exact required CF)
2. 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

- Value 10-year zero = (4.611/10)*91575=\$42,222SEL
- How many? P= 1000/1.06^10 = \$558.39
42,222/558= 75.6 units be sold
2. ALTERNATIVE
DV01= (915.75*4.61/1.06)/10000 = 0.398
DV01= (558.39*10/1.06)/10000 = 0.527
100(0.398)+n(0.527) = 0; n = -75.61 (same result)

Assume:
- flat yield curve
- parallel shift of yield curve
- linear approximation

(1 )P
Duration is in
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