Frequently Asked Questions

This is the rate of return anticipated on a Bond, if it is held until the maturity. YTM is computed on the assumption that coupons (interim interest payments) will be reinvested at the same rate as the quoted YTM. It is an indicative measure of the return of the bond. It is important to note that you may not be able to invest the Bond coupons at the same YTM quoted at the time of purchase and this may result in the total investment yield being less than the original YTM rate. The calculation of YTM is identical to the calculation of Internal Rate of Return

- If a bond's coupon rate is less than its YTM, then the bond is selling at a discount
- If a bond's coupon rate is more than its YTM, then the bond is selling at a premium
- If a bond's coupon rate is equal to its YTM, then the bond is selling at a par

No you don't get 2 interest rates. Coupon rate is a percentage of the face value determined at the time of issuing a Bond. Coupon payments are paid semi-annually on Treasury Bonds issued by the Central Bank of Sri Lanka. YTM is the rate that indicates your return on the investment.

Yes. As mentioned, the coupon rate is a percentage off the Bond's face value. Since the coupon payments are semi-annual, we need to divide the coupon rate in half. Let's calculate a coupon payment using an example:
Face Value of the Bond = LKR 1,000,000 Maturity Period = 2 Years Yield to Maturity = 12%p.a. Coupon Rate = 10%p.a. paid semi-annually Semi-annual coupon payment = {1,000,000 x (10% / 2)} = LKR 50,000

Bonds are invested for durations longer than 1 year. Investors normally expect at least an annual cashflow from their investment like dividends on shares. This indicates amongst other things that the borrower is solvent or is able to service its debt. Although there are coupon-less bonds on issue (on popular in Sri Lanka) called 'zero coupon bonds', coupon bonds, of which semi annual paying bonds have become the most popular type of bonds in the world.

No. Settlement value is derived by discounting future cash flows of the Bond to present value. One of the major assumptions of the Bond yield calculation is that coupon payments will be reinvested at the original yield until maturity, which is almost certainly not the case in reality. This is not captured if you merely add the coupon payments to the settlement value of the Bond.

Yes. You can sell the Treasury Bond in the secondary market [to a primary dealer or commercial bank] and exit the investment prior to its maturity. However, depending on the market interest rates and the period to maturity there is a possibility you may incur a capital loss or a gain, if the Bond is sold before maturity.

Yes. You can determine how much you wish to sell in the secondary market.

Bonds in the secondary market are often traded in between coupon payment dates and the Bond seller must be compensated for the portion of the coupon payment he/she earns for holding the Bond since last coupon payment. This is because irrespective of when the secondary market sale happens, coupon interest is paid on the initially specified coupon payment date to its present Bondholder. The Dirty Price refers to the real value of the Bond or the net present value of cash flows for bond with a face value of 100/-. The Clean Price refers to the value that has removed the accrued coupon from the Dirty Price. In the bond markets, when traders refer to the price of a bond, they are almost always talking of the clean price. Accrued interest can be calculated directly from the Bond's details and the market lets the buyers to work out the Dirty Price.

Let's look at an example where a Bond issued on 1st January 2008 is sold by a customer after 134 days and the next payment is expected July 1: Face Value of the Bond = LKR 1,000,000 Maturity Period = 2 Years (From 1st Jan 08 to 1st Jan 10) Yield to Maturity = 12%p.a. Coupon Rate = 10%p.a. paid semi-annually.

1. To determine the semi-annual coupon payment, we divide the coupon rate in half, which gives a rate of 5% (10% / 2). Each semi-annual coupon payment will then be LKR 50,000 (LKR 1,000,000 x 5%) 2. We then determine the number of days since last coupon payment: From 1st January to 14th May 08 = 134 Days There are 48 days remaining before the next coupon payment and the Bond seller has accumulated 134 days worth of interest (182-48). 3. Accrued interest is a fraction of the coupon payment that the seller has earned:

You simply pay the net present value of all cash flows. This is represented by the Dirty Price for a bond of 100/-. The accrued interest and clean price are terms usually relevant to professional traders.

Duration measures how long, in years, it takes for the price of a Bond is repaid by its internal cash flows. For investors, it is an important measure to consider, as Bonds with higher duration carry more risk and is highly affected by price volatility. Hence, it helps you to determine how you can protect your portfolio from interest rate risk. Duration is not the same as tenor. In other words, it is a weighted average of the "life" of a Bond and as coupons are being paid to the Bondholder, duration shortens. This is because, as you receive a coupon payment, it is no longer counted as a future cash flow that goes towards repaying what you have invested initially Duration allows the investor to compute the sensitivity of the price of the bond to a the change in yield. The formula is as follows: Price Change = Yield Change X Duration Please note this is only an approximate sensitivity check and the more accurate sensitivity check will involve the use of modified duration (see below) and convexity. This is more appropriate for bond portfolio management.

Let's look at the following diagram which considers a 2 year Bond that pays coupons semi-annually. Its cash flows have 4 coupons and the redemption value or the face value.

Notice that to balance the lever where total cash flows equal the amount paid for the Bond, the lever must be kept to the right, at a point before maturity. As you receive a coupon payment, it is no longer counted as a future cash flow that goes towards repaying the Bondholder: hence, the lever is no longer in balance. The lever now must be moved further to the right in order to balance the timeline but notice how the timeline is now shortened (4 payment periods reduced to 3):















Therefore, duration decrease as time moves closer to maturity. If there is only a single cash flow, the duration = time to maturity.

Macaulay duration replaces the above simple cash flows with the present value of each cash flow on the scale. This is a better measure of price sensitivity than simple duration as it gives due to weight for near cash flows as opposed to the further cash flows, i.e. Rs. 5/- in 6 months should not have the same weight as the Rs 5/- in 24 months. Example: Face Value of the Bond = LKR 1,000,000 Maturity Period = 2 Years Yield to Maturity = 12%p.a. Coupon Rate = 10%p.a. paid semi-annually

Cash Flow 1	Cash Flow 2	Cash Flow 3	Cash Flow 4
C/t     (1 + R/t)	C/t     (1 + R/t)2	C/t     (1 + R/t)3	Principal + C/t    (1 + R/t)4
100,000/2    (1 + 0.12/2)	100,000/2   (1+ 0.12/2)2	100,000/2  (1 + 0.12/2)3	1,000,000+(100,000/2)  (1 + 0.12/2)4
50,000       1.06	50,000      (1.06)2	50,000      (1.06)3	1,050,000      (1.06)4
47,169.81	44,499.82	41,980.96	831,698.35	965,348.94
0.5 x 47,169.81	1.0 x 44,499.82	1.5 x 41,980.96	2.0 x 831,698.35
23,584.91	44,499.82	62,971.44	1,663,396.70	1,794,452.87
Macaulay Duration	1,794,452.87  = 1.88 Years  965,348.94

The price sensitivity varies depending on the interest rate that is used to measure price change. For example the price change for a yield change at 10% to 11% is different from price change for a yield change from 20% to 21%. This is simply due to the relative change, i.e. at 10% the 1% change represents a 10% change from the base rate, while at 20% the 1% change represents only a 5% change from the base rate. Modified duration is used to approximate for this effect by using the following formula. Modified Duration = Macaulay Duration 1 + (YTM / Number of Coupons per Year) Modified Duration = 1.88. = 1.77 years 1 + (0.12 / 2) Basic Rules on Modified Duration: Higher the YTM, lower the Modified Duration; therefore lower the price sensitivity. Lower the YTM, higher the Modified Duration; therefore higher the price sensitivity. Higher the Coupon lower the Modified Duration; therefore lower the price sensitivity. Lower the Coupon, higher the Modified Duration; therefore higher the price sensitivity.