What is Effective Duration?
Effective duration is a duration calculation specifically designed for bonds that come with embedded options. This measure accounts for the fact that the expected cash flows from these bonds will fluctuate as interest rates change, thereby serving as a risk metric.
Key Points:
- Effective duration caters to bonds with embedded options.
- The uncertainty of cash flows in such bonds complicates their rate of return estimation.
- Effective duration assesses the impact on cash flows as interest rates vary.
- It also calculates the expected price decline of a bond when interest rates rise by 1%.
Grasp the Concept of Effective Duration
When a bond has embedded features, like a callable or puttable option, the predictability of its cash flows diminishes, making it challenging to pinpoint its rate of return. Effective duration aids in calculating how sensitive these bonds are to changes in interest rates as reflected by the yield curve. Notably, effective duration gauges the expected price drop of a bond in response to a 1% rise in interest rates.
Calculating Effective Duration
To get a grasp on how effective duration is computed, here’s a simplified formula. The variables include:
- P(0): Original price per $100 of par value.
- P(1): Price if the yield decreases by Y percent.
- P(2): Price if the yield increases by Y percent.
- Y: Estimated change in yield used to compute P(1) and P(2).
The formula is:
Effective duration = (P(1) - P(2)) / (2 x P(0) x Y)
Practical Example
Suppose an investor purchases a bond at 100% par currently yielding 6%. By changing the yield by 10 basis points (0.1%), the bond’s price drops to $99.25 if the yield increases, and it rises to $101 if it decreases. Thus, the effective duration is:
Effective duration = ($101 - $99.25) / (2 x $100 x 0.001) = $1.75 / $0.20 = 8.75
So, an effective duration of 8.75 signifies that a 1% shift in yield translates roughly to an 8.75% change in the bond’s price. For a more accurate estimate, the bond’s effective convexity can also be considered.
Related Terms: duration, modified duration, yield curve, rate of return, option-free bond, callable bond, convexity.
References
Get ready to put your knowledge to the test with this intriguing quiz!
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## What does effective duration measure?
- [x] Interest rate sensitivity of a bond or a portfolio
- [ ] Credit risk of a bond or a portfolio
- [ ] The liquidity of a bond in the market
- [ ] Default probability of a bond issuer
## Which element is crucial for calculating the effective duration?
- [ ] Credit rating of the issuer
- [ ] Corporate governance structure
- [x] Changes in yield
- [ ] Maturity date
## Effective duration is specifically used to address which kind of bonds?
- [ ] Zero-coupon bonds
- [x] Bonds with embedded options
- [ ] Bonds issued by the government
- [ ] Convertible bonds
## What does a higher effective duration indicate?
- [x] Greater sensitivity to interest rate changes
- [ ] Lower sensitivity to interest rate changes
- [ ] Greater credit risk
- [ ] Shorter maturity
## Which is an example scenario to use effective duration?
- [ ] Valuing real estate
- [x] Managing bond portfolios for interest rate risk
- [ ] Assessing stock market trends
- [ ] Forecasting GDP growth
## In which scenario might effective duration provide a more accurate measure than modified duration?
- [x] When dealing with bonds with prepayment options
- [ ] When calculating interest rate sensitivity of government bonds
- [ ] When evaluating zero-coupon bonds
- [ ] When focusing on credit rating changes
## How does a call option affect the effective duration of a bond?
- [x] It can reduce the effective duration
- [ ] It can increase the effective duration
- [ ] It has no effect on effective duration
- [ ] It quadruples the effective duration
## Effective duration considers which of the following?
- [x] Expected cash flows in response to yield changes
- [ ] Historical bond prices
- [ ] Bond market liquidity
- [ ] Corporate profitability
## Which formula component adjusts for cash flow changes in effective duration computation?
- [ ] Present value of cops
- [x] Expected cash flows
- [ ] Dividend payouts
- [ ] Market capitalization
## What is generally the independent variable in the effective duration formula?
- [ ] Bond maturity
- [ ] Bond issuer's stock price
- [x] Yield curve changes
- [ ] Inflation rate
