*This article appeared in Capital page of The Edge Malaysia, Sep 27 - Oct 2,2010*

**By Jasvin Josen**

Malaysia was in the limelight in June this year when its global Islamic Note (or Sukuk) was oversubscribed by over four times. The 5-year bond was awarded a stable rating of “A-“ by Standard & Poor ‘s and “A3” by Moody’s and managed to attract a yield of 3.928%, just 180 basis points (1.8%) over 5-year U.S. Treasuries. On Aug. 25, Bloomberg reported that the yield had dropped to a record- low of 2.63%. Concurrently, the yield on Indonesia’s 2014 Sukuk also reached an all-time low of 2.543% on Aug. 19.

What does the yield represent and why is a drop in yield perceived as good news? In this article, I will describe some basic characteristics of bonds in general before advancing to specific aspects of sovereign bonds. Islamic bonds and its unique features will be left for discussion at a later stage.

**The time value of money**

Time value of money plays a critical role in the pricing of any financial instrument. In a nutshell, the further the money is to be received in the future, the less that money is worth today. Say Investor A buys a bond from an issuer. At the onset, he pays $100 to the issuer and receives the bond, which is essentially the issuer’s promise to repay the loan. Say the bond promises to pay a coupon of 5% at the end of Year 1 and Year 2, with the principal repayment also at the end of Year 2.

If one were to value the bond at the beginning of Year1, he has to discount the money that he will receive in the next two years. This is because; the total sum to be received of $110 ($5 + $5 +$100) could have been received now and put into a savings account to earn some interest. Therefore the investor has lost the chance of earning that interest on his money.

It is this interest lost that forms the crux in measuring the time value of money. Say the annual interest rate for savings accounts is 3%. In one year’s time, $100 would have grown to $103 ($100*1.03). At the end of year two, $103 would have grown to $106.09 (103*1.03). These can be simplified as follows:

[106.09 = 100 (1+0.03)

^{2 }]or more generally:

**FV = PV (1+r)**

^{n}Where: FV = Future value of money

PV= Present value of money

r = interest rate

n = years in question

From a reverse perspective, if we were to analyse the present value of $106.09 today, to be received in two years time, we would discount the money as shown in

**Chart 1.****Chart 1 – The present value of money**

Back to the bond in question, the investor will need to discount the moneys to be received from the bond using the same principle. The present value of the bond which is also the price of the bond, is computed in

**Chart 2**.**Chart 2: Computing the present value of a bond**

The pricing formulae in

**Chart 2**can be further generalised to price any bond, as shown in

**Chart 3.**

**Chart 3: Pricing a Bond**

Where C = annual coupon on the bond

F = principal or face value of the bond

y

_{1}, y_{2 }= market discount rate of the bondTo recap, when interest rates are 3%, the bond is worth $103.83 to the investor (refer

**Chart 2**). If interest rates were to go up, the investor stands to lose more money on foregone interest. Intuitively there would be less demand for this 5% coupon bond, bringing the price down. Mathematically, this is exactly what happens; as “y”, the discount rate is higher, the present value of the bond falls. Thus we see that the price and discount rate have an inverse relationship.Interest rates do not have to be the same every year. If there is sentiment that interest rates will go up in Year2 to 4%, the investor will use y

_{1}as 3% and y_{2}as 5% when valuing a bond, in**Chart 3.****What does the discount rate represent?**

The discount rate is the core of bond pricing. In a non risk-free world that we live in, the discount rate represents more than just the interest rate. Back to our earlier example, say that due to adverse market news, Investor A is now worried about the ability of the issuer to pay the coupons and the principal at maturity. He and all other investors will not want to hold the bond and would look to sell the bond, presumably at a much lower price than $103.83. The lower price will push the discount rates up to a rate higher than 3%.

Now the discount rate will be made up of the 3% interest rate and another factor, called the credit spread. Credit spread largely represents the default risk of the issuer.

**What is yield to maturity?**

The market prefers to refer to the discount rate as “yield” and often uses this yield to measure the performance of bonds, rather than price. So how do we find the yield as the bond price moves in the market? A popular approach is to find its “yield to maturity”. This approach simply assumes that the bond has the same discount rate (or yield) every year. In market terms, it has a flat term structure. One can simply refer back to

**Chart 3**, accommodate for y_{1}=y_{2}=y, and the adjusted formulae will look like**Chart 4.**Say the bond price plunged to $98 two days after inception. Putting this price in the formulae in

**Chart 4,**( PV=98, C=5, F=100), we will get a yield (y) of 6.09%. This flat yield of maturity assumes that investors are assuming the same discount rate every year. In reality we know that this is not true as yields (made up of interest rates and credit spreads) do not have to be constant from year to year. However, this approach is the most practical and accepted by the bond market to measure bond performance.**Chart 4: Finding the Yield to Maturity**

**Why are high yields and high prices considered good?**

It depends on your perspective. If you are a bond investor, high yields are what you desire because you want to pay $98 for that $100 bond. However, if you are a bond-owner, you are now going after price. You have already locked in your yield, and if the price rises you will sell the bond and make a profit.

**Why is low yield considered a good thing as well?**

When bond prices are high, it means they are in demand. With the inverted price-yield relationship, these bonds will have low yields. As yields are made up of interest rates and credit spreads, low yields also imply that investors expect a low default risk of the issuer.

The recent low yields exhibited by Malaysian sovereign bonds (Malaysian 5-year government securities (MGS) also have been having low yields, below 3.5%) are occurring at a time where the other part of the globe is undergoing serious downgrades and a steady rise in yields.

**Sovereign Bonds – main factors affecting the change in credit spreads**

We know that credit spreads form a major component of yields and credit spreads largely point to the default risk of the issuer. However studies have shown that while this is probably true for corporate bonds, it does not stand well with sovereign bonds. In fact, a study [Gruber, Agrawal, and Mann, 2001] found that default risk only explains 25% of the change in credit spreads.

A paper in 2001, “The Determinants of Sovereign Bond Credit Spreads Changes” by Michael Westphalen discovered that while the main factors like changes in default risk and volatility were significant, they collectively only explained 10-20% of the variation in credit spreads.

The unique point about sovereign bonds is that they cannot be liquidated. The Argentine bond default in 2004 and the recent Dubai World bond default in 2009 resulted simply in a restructuring exercises, largely on terms of the sovereigns rather than the investors.

The closest solution is perhaps litigation. The study found new factors like fraction of principal that could be recuperated through litigation. The lower the fraction, the higher the risk of default and the higher the credit spread. The essence is that since sovereigns can only be litigated and not liquidated, there is a higher risk premium demanded by investors for this peculiar risk.

**Conclusion**

It is hoped that this article has enlightened the reader on principles of bond pricing, specifically the time value of money, the meaning of bond yields and how to compute them, and the inverse price-yield relationship in bonds. As for sovereign bonds, unlike corporate bonds (theoretically at least) investors seem price in a premium to compensate for the fact that sovereigns cannot be liquidated upon default.

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