## Tuesday, February 26, 2013

### CD rollover risk

Question:  A person must decide between investing in a CD for 10 years now or investing in a CD for 5 years now and rolling over at the interest rate prevailing after the five-year period.  Let’s assume the current interest rates are 0.5% for a 5-year CD, and 1.5% for a 10-year CD.

How much would an investor have after 10 years from investing in a 10-year note?

Assume interest rates remain unchanged in 5 years.  How much would an investor have if he invested in a 5-year note now and he reinvested in a 5-year note at maturity?

Assume that in five years the new 5-year CD rate is 4.0%.   How much would the investor have if after five years he rolled the 5-year note over into another 5-year note at the prevailing 4.0% interest rate?

Would you choose investing in the 5=year note now and rolling over at an uncertain interest rate in 5 years or would you rather invest in the certain 10-year CD?

Answer:  The formula for the future value of a CD with an initial balance A invested at interest rate r after n years is

FV=Ax(1+r)n

Use this formula to obtain the future value of the CD under the different investment strategies.

We consider a \$1,000 initial investment.

At n=10 and r=0.015 the investor in a 10-year CD will receive  \$1,161 after 10 years.

The investor who purchases the 5-year CD and rolls it over will receive \$1,051 if interest rates remain unchanged after 5 years.  (Plug in n=5 and r=0.005.  Put the balance after 5 years (\$1,025. 25) into the formula with the n=5 and r=0.005.)

The investor who purchases the 5-year CD and rolls it over at a new interest rate of 4.0% in five years will have \$1,247 after 10 years. (Put the balance after 5 years into formula for a 5-year CD at 4.0%.

The choice of investment strategy is a complex question that is only partially addressed by perceptions of future interest rates, Many people believe that interest rates are highly likely to rise and that too many people are chasing yield by investing in longer assets.  Allan Sloan wrote a nice article on this topic.  You may want to look at my post describing Allan’s argument.

More thoughts:  Interest rates are really hard to predict.  I am not too worried about higher rates in the next year but a lot can happen in a decade and the interest rate scenario considered in this post is really quite modest when one considers past interest rates.  The analysis presented here may understate potential gain from remaining liquid if interest rates rise.

You may need the money in 5 years. There is a cost in less liquidity from locking money up for a longer period of time.  In my view, the interest gain from investing in the 10-year CD is not worth the risk and the loss of liquidity.

(Allan Sloan’s calculations are based on bonds rather than CDs.  Bond investors realize a capital loss if interest rates rise and they sell.)