Declining Bond Price at Maturity Versus Sold Today

A few weeks ago I responded to a comment for a reader on one of my bond posts regarding a fear of loss of bond principle when holding bond funds. As I responded to that comment I realized this might be a good topic to expound on as I know most people do not understand this particular topic. The loss of principle the reader was referring too was related to selling a bond before maturity. The topic for this post therefore is to speak to why Declining Bond Price impact on Bonds Held to Maturity Versus Bonds Sold is the same regardless of when you sell. It does not matter if it is to maturity or this moment.

How are Bonds Priced?

So lets start by talking for a moment about how are bonds are priced. So say I have a bond bought at face value (also known as par). This means I’ve bought the bond for what it will be worth at maturity. Now imagine that par bond, lets say it cost you 1000 dollars for a bond worth 1000 dollars at maturity. It has a coupon worth a 3% return. (An aside, you can learn more about coupons in this post.

Now imagine you have a second bond. All other conditions are equal: the economy is the same, the risk rating of the bond is the same, the issuer is the same, the calculability is the same, and even the duration of the bond is the same. Due to the efficient market theory, all other things being equal a 1000 dollar bond costing 900 dollars should have a lower coupon then the bond costing 1000 dollars. Why?

Why do Bond Prices Relate to Coupons?

In either case the 1000 dollars in face value returns 30 dollars a year in coupon. In either case when you are done with the bonds at maturity they are both worth 1000 dollars. So the 900 dollar bond would be worth both the coupon rate provided plus the discount on the bond. These two combined would be more to the investor then the 1000 dollar bond’s coupon alone. As such if it had the same coupon rate no one would buy the 1000 dollar bond. As such in order for the second bond to have the same coupon all other things equal it has to have the same price. Or to have the same price all other things equal it must have the same coupon.

Bond Price in Relation to the Environment

Now that we understand the movement of the parameters in a steady state environment, lets go the other way. Imagine I have one bond worth 1000 dollars sold at par. It had a coupon of 3%. Now imagine inflation rose and inflation expectations increased. Suddenly you can buy a new bond at par under the same terms with a 4% coupon.

The question becomes why would anyone ever buy your 3% coupon bond? Simply put they would only if you reduced the cost to make up for the lower coupon rate. To sell you would need to reduce the cost, or give a discount on the value of the bond. The discount provided would be equal to the present value of the difference in coupons between the two bonds. I.E. it would be tied to the value of making 4% instead of 3% each year of the bond. The bond’s price thus moves inverse to it’s yield. The price decreases when yields of the other bonds on the market, as visible by at par coupons, increases. The bond price increases when yields of the other bonds on the market, as visible by at par coupons, decrease.

Declining Bond Price impact on Bonds Held to Maturity Versus Bonds Sold

The implication of bond prices moving inverse to yields is that the price of the bond has essentially declined proportionately to the change in market yields. As such by definition your overall financial well being is the same whether you sell when the yield changes or hold until maturity. You are either paying for the reduction today based on the present value in the decline in price. Or you pay for the reduction later in the form of the future value of the decline in coupons. Da$ned if you do, Da$nd if you don’t.

A Caveat on Equality

The above theory assumes zero cost of trading a bond. In practice you have commissions added to bond price. You also have spreads. These costs of trading create a difference between what the bond is worth based on the above theory and what you can actually sell it for. These two items make actually selling early more costly then holding to maturity where you typically do not pay commissions or spreads. As such I rarely recommend selling an individual bond early.

The Caveat in Respect to Bond Funds

Here is where it gets interesting. The difference between you holding one bond and a bond fund holding millions significantly changes the impact of trading costs. Of course a bond fund will have to sell some bonds in order to make up for fund redemptions by fund holders. You get a choice on whether to sell. However, a bond fund can choose which bonds to sell to minimize the impact of trading costs. It also has market making power because of economies of sale. I.E. a bond fund does so much business in bonds that by it’s nature it can reduce spreads and commissions.

Finally, because it constantly buys and sells it benefits from spreads often in the same ways it is harmed by spreads. They largely even out over time leaving commissions as the primary cost. Given how closely these bonds track their indexes and how low their expense ratios are, this theory largely holds.  Bond funds seem to be priced based on the price of their underlying holdings.  Trading costs appear to have minimal effect.

Conclusions Regarding Bond Price

Based on the above there is no significant difference between bond funds and individual bonds from a rate change perspective. Both have the same disadvantages in relation to the duration of the underlying holdings.  This was my response to my reader during that bond fund discussion, however in a much more abbreviated way. Hopefully the details here give you more confidence in bond funds versus bonds in a rising rate environment. I believe the benefit of diversification of the bond funds to reduction in risk is worth it regardless of the rate environment. At very least you now understand the Declining Bond Price impact on Bonds Held to Maturity Versus Bonds Sold is the same.