What is the formula for duration?

What is the Duration Formula? The formula for the duration is a measure of a bond’s sensitivity to changes in the interest rate, and it is calculated by dividing the sum product of discounted future cash inflow of the bond and a corresponding number of years by a sum of the discounted future cash inflow.

How do you calculate the duration of a loan portfolio?

Portfolio duration is commonly estimated as the market-value-weighted average of the yield durations of the individual bonds that compose the portfolio. The total market value of the bond portfolio is 170,000 + 850,000 + 180,000 = 1,200,000.

How do you calculate duration and modified duration?

To find the modified duration, all an investor needs to do is take the Macaulay duration and divide it by 1 + (yield-to-maturity / number of coupon periods per year). In this example that calculation would be 2.753 / (1.05 / 1), or 2.62%.

How do you calculate effective duration?

Effective Duration Calculation P(0) = the bond’s original price per $100 worth of par value. P(1) = the price of the bond if the yield were to decrease by Y percent. P(2) = the price of the bond if the yield were to increase by Y percent. Y = the estimated change in yield used to calculate P(1) and P(2).

What is a portfolio duration?

The sensitivity of a portfolio of bonds such as a bond mutual fund to changes in interest rates can also be important. The average duration of the bonds in the portfolio is often reported. The duration of a portfolio equals the weighted average maturity of all of the cash flows in the portfolio.

Why do we calculate modified duration?

Modified duration is a price sensitivity measure and is the percentage change in price for a unit change in yield. Modified duration is more commonly used than Macauley duration and is a tool that provides an approximate measure of how a bond price will change given a modest change in yield.

What does Macaulay Duration indicate?

Macaulay duration, named after Frederick Macaulay who developed the concept, is a measure of how long it takes for the price of a bond to be repaid by the cash flows from it. The Macaulay Duration of a debt fund is nothing but the weighted average Macaulay Duration of the debt securities in the portfolio.

What does effective duration tell?

Effective duration calculates the expected price decline of a bond when interest rates rise by 1%. The value of the effective duration will always be lower than the maturity of the bond.

How can I reduce my portfolio duration?

Adjusting the total modified duration of a portfolio to investor’s specifications is simple with the help of futures contracts. By selling (or buying) futures contracts, it is possible to decrease (or increase) the total modified duration of the portfolio.

How do you calculate modified duration in Excel?

The formula used to calculate a bond’s modified duration is the Macaulay duration of the bond divided by 1 plus the bond’s yield to maturity divided by the number of coupon periods per year. In Excel, the formula used to calculate a bond’s modified duration is built into the MDURATION function.

Which fund has Macaulay Duration in between 1 to 3 years?

Short duration funds are debt mutual fund schemes which invest in debt and money market securities such that the Macaulay Duration of the scheme is 1 to 3 years. The investment objective of these funds is income generation through accrual over the maturity term of the instruments in the scheme portfolio.

What is one sided up duration?

The “up” and “down” refers to the interest rates, not bond prices. So to say that callable bonds have higher “up” duration means that when interest rates go up, prices fall, and the bond is less likely to be called (and more likely to run through maturity –> higher duration).

What is the formula for calculating days in Excel?

Calculating the number of days using Excel is pretty simple. Just use a formula to subtract the later date from the earlier date. For example, if cell A1 contains 1-Jan-2004 and cell A2 contains 03-Mar-2004, you simply enter the formula =A2-A1 in cell A3 to get the number of days.

How do you calculate KRD?

As mentioned earlier, the sum of the KRD values K = K 1+K 2+… +K N must equal (B΄ –B΄ +)/(2δ), where B΄ – and B΄ + are the bond prices resulting from a downward and respectively upward parallel shift of the base yield curve, whereby all input zero rates are shifted simultaneously by the given one sided rate shift δ.

What is the callable bond’s one sided up duration?

Moosey: Up duration of a callable bond is higher than its down duration. Only when convexity is negative; i.e., at low interest rates. When interest rates are high (and the option is out of the money), up duration is lower than down duration.