Archives for July 2016

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Why Do Bond Prices Work the Way They Do?

A reader writes in, asking:

“I know that interest rates and bond prices move in opposite directions, but I don’t honestly understand why that is the case. And while we’re at it, why do bond funds with a long duration have bigger price fluctuations than bond funds with a short duration?”

Imagine that you buy a $1,000, 10-year Treasury bond, with a 2% coupon rate. (That is, it pays $20 of interest per year.) And you hold that bond for five years, such that it is now effectively a 5-year Treasury bond with a 2% coupon rate.

And imagine that, over those five years, interest rates have risen, and newly-issued 5-year Treasury bonds are now paying 3% interest.

In such a scenario, if you wanted to sell your bond for $1,000, you’d have a very difficult (i.e., impossible) time. Nobody would want to buy your bond with its 2% interest rate, when they could just buy new 5-year bonds with a 3% interest rate instead. In order to sell your bond, you’d have to sell it for less than $1,000. That is, its price has gone down because interest rates have gone up. (Specifically, you would have to sell your bond at a sufficient discount that it would offer the same yield to maturity as newly-issued bonds of the same duration.)

And the same sort of thing happens in reverse. Imagine instead that rates on 5-year Treasury bonds had fallen to just 1%. In that case, people would be willing to pay more than $1,000 for your bond with its 2% coupon rate. That is, interest rates fell, so the value of your bond went up.

Why Do Longer-Term Bonds Have More Interest Rate Risk?

When interest rates change, the price of a bond fund will move (in the opposite direction) by an amount approximately equal to the average duration of the fund, multiplied by the percentage change in applicable interest rates. For example, if the whole Treasury yield curve were to rise by 2%, a Treasury bond fund with a 3-year average duration would fall in price by roughly 6%, and a Treasury bond fund with a 7-year average duration would fall in value by roughly 14%.

But why do longer-duration bonds experience more severe price fluctuations? Without getting into the underlying math*, I think the concept is most easily understood with an example.

Imagine that on a given day you purchase a 1-year Treasury bond and a 20-year Treasury bond, both of which you plan to hold until maturity. Then, on the very next day, the entire Treasury yield curve moves upward by 1%.

  • Holding the 1-year bond to maturity means you’ll be collecting a subpar interest rate (i.e., missing out on an additional 1% yield, relative to new bonds) over the next year.
  • Holding the 20-year bond to maturity means you’ll be collecting a subpar interest rate each year for the next twenty years.

Missing out on an additional 1% yield for a year isn’t great of course. But missing out on 1% per year for twenty years is a much bigger deal. And that is essentially why longer-duration bonds have larger price fluctuations when current interest rates change.

*For those who are interested in the technical explanation: The market value of a bond at any point in time is equal to the sum of the present values (i.e., discounted values) of each of the future cash flows the bond holder will receive. When market interest rates change, the discount rate we use to calculate present value changes. And a given change in discount rate (e.g., 1% higher or lower) has a much greater effect on cash flows far in the future (such as you would receive with a long-term bond) than cash flows in the near future.

How Many Mutual Funds is “Too Many”?

A reader writes in, asking:

“I read your book investing made simple. The book does not mention how many  funds are too many to have in a portfolio. Do you think 9 funds is too many to have in my 403b portfolio?”

There is no broadly applicable, definitive answer for how many funds is “too many.”

The only time that a portfolio could be clearly, objectively said to have too many funds is when the portfolio includes a fund that serves no purpose, because it does nothing other than duplicate other funds in the portfolio. For instance, if an investor had an IRA that included:

  • Vanguard Total Stock Market Index Fund,
  • Vanguard Total International Stock Index Fund, and
  • Vanguard Total World Stock Index Fund…

…then it would be clear that this investor has “too many” funds, because the same overall allocation could be achieved using fewer funds. That is, any desired domestic/international breakdown can be achieved using the Total Stock Market and Total International index funds — no need to include the Total World index fund as well. (Alternatively, if the investor is happy with the domestic/international breakdown included in the Total World index fund, he/she could use only that fund and eliminate the other two funds.)

So, at least in my view, pointless duplication of holdings is the only time that a portfolio would objectively, clearly include “too many” funds.

There are many cases, however, in which an investor could say, “this is too many funds for me.”

That is, some investors (myself, for instance) place a high value on simplicity and do not care so much about being able to custom-tailor their allocation in various ways, so they use a single all-in-one fund (e.g, target retirement or Vanguard LifeStrategy fund) for their portfolio.

Conversely, some investors don’t at all mind managing a portfolio of many holdings, and they do care quite a bit about holding some very specific asset allocation (e.g., overweighting certain groups of stocks in their portfolio by holding a REIT fund, small-cap value fund, etc.), so they will select a portfolio consisting of several different funds.

And some investors are somewhere in the middle of that spectrum, preferring to use something like the “three-fund portfolio” often discussed on the Bogleheads forum (made up of a domestic total stock market index fund, an international total stock market index fund, and a diversified bond index fund).

Any of the above approaches can be perfectly rational — it’s simply a matter of personal preference.

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