CD Rates are REALLY LOW!

[unclemick]

Hey Ted
Great post. Now the other concept which I have difficulty with keeping straight is "duration" both for a single bond and a bond fund. The longer the duration the greater the change in market value with interest rate change - right?

 

[Ted]

Unclemick,

You're basically right about duration, and here's how it works more specifically (but without rigorous mathematical proof).

To calculate the duration of a bond, all of the future payments (both interest payments and payment of principal at maturity) are converted to present worth values.  The duration is the average length of time to the payments, weighted by the present value of each payment.

The duration is always less than the time to maturity, except in the case of a "zero coupon" bond, which makes no interest payments.  This type of bond makes only one payment -- at maturity -- and so its duration is equal to its time to maturity.

The practical value of the "duration" parameter is that it provides an easy indication of the sensitivity of a bond's market price to changes in interest rates.  The market value will change (in the opposite direction of interest rates) by a percentage that is given by the change in the interest rate multiplied by the duration of the bond.  For example, if the interest rate on bonds with a duration of 10 years increases by 1 percentage point, the current market value will drop by 10 percent.  I don't think that this is mathematically precise, but it's close enough to be of practical value in understanding your exposure to the risk of changes in the market value of bonds as interest rates change.

By the way, the duration of a portfolio of bonds is just the average of the durations of the bonds in it, weighted by their market value.

An editorial comment:

Consistent with the economic principle that "there's no such thing as a free lunch," the increased risk of short-term loss of market value that comes with bonds of longer duration, is the "price" that investors pay for receiving higher long-term rates of return.  The people complaining about the low returns on short-term bonds (those with very short durations) are like people in hell complaining that they don't get icewater.  

 

[unclemick]

Thanks Ted
Hope your two posts stay up for a while so I can refer back to them.My mental block is that 1977- 1993 the company 401k allowed me to to fifthy-fifthy S&P 500/GIC's(guaranteed investment contracts) after reading Ben Graham's The Intelligent Investor. I still need to periodically refresh my brain when it comes to bond price movements.Like previously mentioned buying a balanced fund 'out of can' allows me to duck the issue until I tryed to bump up income a little.

 

[haha]

To calculate the duration of a bond, all of the future payments (both interest payments and payment of principal at maturity) are converted to present worth values. The duration is the average length of time to the payments, weighted by the present value of each payment.

Ted, thanks for the concise explanation. I have one further question. What discount rate do you use? The bond's copon rate? The YTM of the bond in question at the date on which you are figuring duration? The coupon on newly issued bonds of similar class? I guess only the bond's coupon rate would give a constant duration. Is duration constant?

Mikey

 

[Ted]

Mikey,

You asked some sophisticated questions that prompted me to refine my understanding of duration. The discounting is done on the basis of the yield to maturity.

When the market price of a bond changes, the yield to maturity will change, and so the duration will change also. (If the bond price drops, its yield to maturity will increase. Therefore, the present value of the principal payment (which occurs at maturity) will drop more than the present value of the interest payments, causing the (shorter) times to the interest payments to be weighted more heavily and the duration to decrease.)

As I suspected, but wasn't certain, the effect of the duration on the sensitivity of the bond's price to interest rate changes is approximate, but good enough for practical purposes since nobody can predict exactly how much interest rates are going to change in the future.

 

[haha]

When the market price of a bond changes, the yield to maturity will change, and so the duration will change also.

Ted, thanks again. Thinking about it, and doing some more reading of my own, I came across an additional way to look at it, suggested by Wm. Bernstein. He says one definition of the duration is the point in time at which you would indifferent as to further rises or falls in interest rates. I think he means that before this time, you will lose more in principle drop, than you will gain in re-investing the coupon at higher rates. After this time, you will be ahead by virtue of higer re-investing, in spite of market price deterioration.

As I think about this, it appears to me that this is one of the many things in finance that apply more to a fund that is managed in perpetuity, with no or modest need for withdrawals. Because if a retired person is consuming his coupon income, all he is going to have left at the end is the face value. I talked about this with my brother, who said it is for this reason that he only invests in ladders of zero's. He decides, is x% pa going to be ok, regardless of what happens in the interim? Clearly one would not want to go too far out, but by watching the yield curve, often a good rate is avaiable at a medium term. So he figures that at worst he gets, say 5% over five or ten years. (Not right now!) At best, rates drop quickly, and he sells for a quick hit.

Just one strategy, that has been quite rewarding for him.

Mikey

 

[Ted]

I hadn't heard the "indifference" explanation of duration before, but it is interesting and makes sense in light of one of the apparent paradoxes of bond investing, which is:

If a person is reinvesting all interest payments (as is especially common for people who have money invested in bond funds) then a rise in interest rates that causes an initial drop in market value will actually net the investor more money in the long run. As Mikey says, the "duration" of the bond portfolio is apparently the break point.

Does this mean that increases in interest rates are "good" for people who own long-term bonds and are reinvesting the interest payments in more bonds? Well, yes and no. The main thing that causes long-term interest rates to rise is an increase in the inflation rate (or at least the market expectation of that, which is usually correct). Therefore, what a long-term bond investor gains in more dollars, they are likely to lose in reduced purchasing power of those dollars.

The idea of "laddering" bonds sounds sophisticated, but all that it really does is to keep the average maturity of the bond holdings approximately constant, usually at an "intermediate" value such as 7 years. A person would get about the same results by investing in an intermediate term bond fund (provided that its expenses are low).

About the only way of insuring that any bond strategy will provide long-term returns substantially in excess of inflation is to invest in TIPs. They are truly revolutionary and are a much better investment than most "financial professionals" acknowledge (other than ones like Jonathan Clements who aren't making commissions by selling some firm's "investment products.")

Historically, long-term corporate and Treasury bonds have delivered returns a couple of percent ahead of inflation, but with a lot more annual variation in total return than is likely to occur with TIPs.