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Thursday, April 26, 2012

Beta and Duration

I was talking with a reader the other night, and we started going over the basic stock metrics that novices need to know.  We started with the P/E ratio which is the most basic measure of all when comparing stocks, portfolios, and even investment philosophies.  In fact, the P/E, which shows how much one is paying for a dollar's worth of earnings, is typically the first number on which stock screening techniques are started.

Differing P/Es need to be reconciled when stock pickers are making buy-and-sell decisions.  For example, if you are comparing company ABC with a P/E of 8 and a company XYZ in the same industry with a P/E of 12, you have to ask yourself why you would pay more for a dollar's worth of earnings in the second case.

The reader and I were on the Yahoo! Finance page and next came to "Beta" as shown here for Deere:
Source: Yahoo Finance

Beta is a basic measure of how volatile a stock, or a portfolio, for that matter, is relative to the market.  A beta of 1 indicates that, on average, a stock will rise percentage wise in tandem with the market.  Thus, if the S&P 500 is up 3.5% and the beta is 1, the stock or portfolio can be expected to be up 3.5%.  It works the same on the down side, of course.

Beta greater than 1 will tend to be more volatile than the market.  For the same 3.5% market return, you can expect Deere to be up 3.5 * 1.48, or 5.18%.  This is an expectation, i.e. an average.  It is obtained by a regression procedure which assumes a certain distribution for returns which, in turn, generates a linear relationship between the market's return and the asset's return.  I know this is more than you care to know.  An important point to appreciate, though, is that it is an expected value.

Duration is Conceptually Similar to Beta

Anyways, bond people didn't want to be left out.  They wanted a measure of how volatile a bond's price is relative to changes in yields.  Luckily, they found that insurance analysts had solved this problem already with a measure called duration.  When you think about it, insurance companies have to figure out the premium to charge for a payout at an unknown future date.  But the value of the premiums over time depend on what happens to yields.  If yields go up, the value decreases; and if yields, drop the value increases.  They have to work it so that, when they include the interest they earn on the premiums, it more than covers the payout.  This is the duration question from another point of view.

So, suppose we consider the most widely used bond ETF, AGG - the Barclay's Aggregate Bond Index ETF.  At Morningstar, we put AGG in the quote box and find (after scrolling down):

Source: Morningstar

This is interpreted as saying that, if yields rise 1% (for example, if the yield on the 10-year rises from 2% to 3%), the price of AGG will drop by approximately 4.36%.  If this is over a 12-month period, you could expect a return of approximately -2.36%, because you will have earned the 2% coupon.

Note also the "Style Map" and how it gives you a grid picture of sensitivity.

As it turns out, the relationship between price and yield for bonds is not linear.  Thus, over time, duration will change; so you will want to check it every few months or so if you are using it to make bond decisions.  Furthermore, the estimate is less accurate the greater the change.  This means that, if you are trying to figure out the impact for a 2% rise in yield, you'll be less accurate.

For homework, check out the duration on TLT, the ETF for longer term Treasury bonds and compare the relative riskiness to AGG.


  1. Thank you for touching on this valuable information. As is usually the case; we come to understand what we do not. Thanks for the info-Derek

  2. An excellent explanation! Thank you for taking the time to share.
    I grew up only learning stocks, then got hammered in the past decade.
    I'm now wishing that I'd known more about bonds a long time ago.
    Bond funds are a very different beast to learn how to invest in than stocks.

  3. You should tie in debt betas and equity betas with modified duration, maybe even convexity

  4. plz Robert can you tell me the comparation between beta and duration on risk and return