The Business Times
Cai Haoxiang
14/10/2013
A FRIEND, upset at how his mother was sold a financial product, recently told me this story.
His mum was convinced by her banker to buy a complex product which involved the bonds of four foreign companies with coupons ranging from 3 to 5 per cent.
Now, 3 to 5 per cent sounds good. But if she knew how bonds worked, she would have asked what the yield of the bonds were.
In this case, her banker did not mention yields at all. Worse still, the product sold was just a derivative on the underlying bonds. The buyer has no legal ownership of the underlying bonds.
My friend cancelled the deal immediately upon finding out. It was unclear what kinds of gains could have come out of it. But it was clear that the bank would make a spread from selling such a product. The banker would make a nice commission. Meanwhile, the risks to the client are complex and might not justify the gains promised.
How do coupons factor into bond pricing? Are higher coupons good?
Before we answer these questions, we have to first understand how bond prices are affected by a major item: interest rates.
The inverse relation
If the US government defaults on its sovereign debt obligations in the coming weeks by failing to raise its debt ceiling, one of the first and most serious consequences will be a rise in interest rates.
This will happen if US Treasuries, previously thought to be the safest asset in the world, face a sell-off.
When investors are not willing to pay as much to lend money to the US government, the US government will need to pay a comparatively higher interest on the bonds it issues to attract investors back.
New bonds will thus yield more for investors. While this can be seen as a good thing, this situation arises because the investors are taking more risk. They are signing up to lend money for a long period of time to a government that might not be able to borrow more to pay them back.
The first relationship in the bond world that beginners learn is the inverse relationship between prices and yields.
When prices fall, yields go up. When prices rise, yields come down.
This can be hard to understand at first. Falling prices is not a good thing for the owners of any asset. So why then do falling prices come with improving yields - which is a good thing?
To figure this out, you have to decide whether you are a bondholder or a potential bond buyer. If you currently own bonds, then falling prices does not seem good because if you really need to sell your investment, you can get less for it.
But falling prices, which are caused by rising interest rates, should not bother you if you have money to reinvest.
After all, you have locked in some gains by buying the bond. You will keep receiving interest payments until the end of the bond's term, by which you will then get the original value of the bond, known as the par value, together with the final interest payment.
If interest rates rise, it just means that your current investment, locked in at an earlier yield, isn't as attractive compared to others now. You won't lose money if you don't sell the bond, assuming the government or company you lent money to does not go bankrupt.
Rather, you can invest more money in bonds at a better yield, now that interest rates are higher.
So while falling bond prices mean that you are sitting on a paper loss, you need not realise the loss, but can continue to hold the bond till maturity and collect the originally agreed-upon interest payments. Most people hold bonds to maturity and are not bothered by fluctuations in between.
Meanwhile, the higher yields that bonds are trading at, given higher interest rates, mean that you can lock in better returns on current investments as a potential bond buyer.
Similarly, rising bond prices are not a good sign for potential bond buyers, for this means that they are not able to get as good a yield on their investments.
But for current bondholders, this means they can sell their bonds for a profit, and reinvest the money elsewhere for hopefully better returns.
Coupons aren't everything
Now we bring in a common feature of bonds that confuse people: coupons.
Coupons refer to the interest payments that issuers of bonds give out, usually twice a year.
For simplicity, we will assume these payments are made once a year. Obviously, the larger the coupons are, the more one would pay for the bond. But if one has to pay a higher price, the bond is not as attractive.
A similar logic applies to how this bond is actually priced.
Let's say a company plans to issue a bond that pays a 10 per cent coupon out of every $1,000 lent to the company. It will borrow $1,000 for 20 years. The $1,000 here is called the face or par value of the bond. This represents the sum of money that the company will repay the investor at the end of the borrowing period.
At a 10 per cent coupon rate, an investor that holds this bond will get $100 every year (10 per cent of $1,000) for 20 years. At the end of the 20th year, he will get the final $100 coupon payment together with the $1,000 face value.
Without even going into the calculations, we can see an investor will get $2,000 worth of coupon payments over the lifetime of this bond.
A 10 per cent coupon thus sounds like a great deal. Right?
Here's the catch.
It usually will not cost an investor only $1,000 to buy this particular bond.
If prevailing interest rates were lower than 10 per cent, a bond with this 10 per cent coupon becomes very attractive. Investors would be willing to pay more to buy it.
The bond's price would typically adjust instantly to a price higher than $1,000. It will trade at a premium.
It will cost an investor way more than $1,000 to get hold of this stream of interest payments of $100 a year.
In fact, if such a deal came out today, and interest rates are 3 per cent - meaning that investors can only get a yield of 3 per cent in the market - this 20-year bond with a 10 per cent coupon will actually cost the investor $2,041 to purchase!
There is no way that the investor can get a yield of more than 3 per cent if 3 per cent was the prevailing interest rate. All bonds issued will lock in a yield of 3 per cent. If their coupons give a higher rate, their prices will automatically adjust upwards.
Thus, it is more accurate to say that investors are willing to pay $2,041 to get a cash flow of $100 a year for the next 20 years, getting back $1,000 in the final year, to get a yield of 3 per cent. This also assumes coupons are reinvested at 3 per cent. Getting the number $2,041 requires a financial calculator. You need to put in the coupon payments every year ($100), the number of years (20), the expected "future value" at the end ($1,000), and the expected interest rate or yield (3 per cent), before computing the "present value" to find out what this stream of payments is worth today.
The 10 per cent coupon rate is not as useful here.
Thus investors have to be wary of only being quoted the coupon rate. They have to ask what the yield of the bond actually is.
Larger coupons lead to lower price volatility
Larger coupons, however, are still useful to have. This is because having a larger stream of regular payments will be a comfort to investors if interest rates change suddenly.
If interest rates change, the prices of bonds with smaller coupons or no coupons will change the most dramatically.
Let's take the example of the previous 20-year $1,000 bond with a 10 per cent coupon, that was issued when interest rates were at 3 per cent.
Once bonds are issued, bond prices will depend on how many coupon payments are left, as well as the interest rate investors can get on other investments.
Ten years in, halfway through the life of the bond, ten $100 payments will have already been made. If interest rates are still at 3 per cent, meaning that investors still expect to yield 3 per cent from similar bond investments, this bond will be worth $1,597.
Now, let us say interest rates spike to 6 per cent. The value of this bond will drop to $1,294 - a 19 per cent drop. If the coupon was just $50 a year, meaning an original coupon rate of 5 per cent, the equivalent price drop will be from $1,171 to $926 - a larger 21 per cent drop.
If the coupon was even smaller, say $20 a year, the price drop will be 23 per cent.
Looking at the yield of a bond is important when buying them, more so than the coupon rate. But in this case, being paid a larger $100 coupon helped cushion the negative price effects of an interest rate spike.
Again, if you don't plan to sell your bond before maturity, this would not make a difference. You would just buy new bonds at higher current yields.
Other effects on bond prices
A lower interest rate environment means more volatile bond prices if there is a rate hike.
If current yields are at 3 per cent, and there is a three percentage-point shock upwards, the bond price of a $1,000 10-year bond paying $50 annual coupons would fall by 21 per cent. If current yields were far lower, at 0.5 per cent, and there was a similar shock to 3.5 per cent, prices would fall by more, 22 per cent to be exact.
This is why the current low interest rate environment means bonds are risky to hold if one plans to sell them at some point.
Another factor that affects the sensitivity of bond prices is the length of time before the maturity of the bond.
If the bond has a long maturity date, meaning there are a lot of interest payments to be made, a change in interest rates would result in a sharper movement in prices.
For example, if the above example of a $50 coupon and 3 per cent yield applied to a 30-year bond, prices would fall by 38 per cent if interest rates spiked 3 percentage points up, higher than the 21 per cent fall for a 10-year bond.
To conclude, coupon rates, interest rate changes, length of maturity and the current interest rate environment all have effects on bond prices.
To measure the sensitivity of the price of a bond to interest rate changes given all these factors, investors use a calculation known as duration. We will discuss this in a future piece.
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