Can I Teach Your Money the Duration Trick?

Even the most sophisticated among us, when a magic trick is performed well, can’t resist its fascination. Let’s admit that. As small kids we thought there was some special power in the hands of the magician. Growing up, we all know that is an illusion, misdirectional cheating. But we keep asking HOW it’s done.

Now, let me show your money the most common of the tricks that time plays to money.

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It’s called the duration trick.

Let’s say your money found an attractive allocation – forgive my patriotism and assume that, last February, that was an Italian fixed income security, the Italian Republic Btp 2.7% 01 March 2047, a coupon bond that would pay a 2.70% annual distribution on the notional capital for 31 years before returning it.

Now the trick.

Please allow me to forgo the complexities (bi-annual payment, rating, changes in the yield curve, etc.) and the precise calculations as they don’t change the substance of the trick – immediate and valid for any coupon bond.

Ok, look at the left hand.

In the left hand there is a contractual maturity of 31-year, during which the bond will pay out a 2.70% of the money invested.

Awesome, 31 years at a return of 2.70% !

This sounds quite right. You are paying par (no discount, no premium), so the annualised return must be 2.70%. And it is… [Simple technical note: as a general rule, any security is quoted at par, i.e. has a traded price of 100, if the expected return and the rate at which the cash flows are discounted are the same].

Hold on now and look at the right hand, waiving the stick.

In the right hand there is a financial maturity, called duration, of 22 years, over which the bond will return 2.70%.

What?  Only 22 years at a return of 2.70%?
How could 9 years disappear?

Well, here’s the trick. And there is neither magic nor fraudulent behavior.

The brain focuses on the basic elements in the left hand: the period of time over which the bond will be in life 31 years, the issue price at par, the 2.70% coupon rate and the stated 2.70% return.

What the brain neglects is that the money paid out as coupon is not yielding 2,70% any more.

That’s called reinvestment risk.  It’s not necessarily a bad thing (although, given the name, it usually is). In fact the cash that exits a transaction usually enjoys lower returns, the risk free rate granted to the liquidity, unless a new (but different and hence unaccounted) risk is taken and a new allocation is started.

It’s the stick, whose waives resume the effect of the time value of money. Only joking… No magic in the stick. It’s just very hard for the brain to visualize that a security that will be in life for 31 years (maturity) is actually worth its rate of return for a much shorter period of time, 22 years (duration).

So it’s never the maturity that matters for financial returns – it is always the duration that does.

What this means is that, at inception, the money allocated to the Italian Republic Btp 2.7% 01 March 2047 bond can expect to become worth

(1+2.70%)^22 = 1.797 x the initial capital,

instead of (1+2.70%)^31 = 2.284 x the initial capital that the contractual maturity may suggest.

What a difference the duration trick makes.

If it doesn’t learn the trick, your money will fall under the powerful illusion of becoming worth more than it actually will be.

And it’s not just with bonds.

The duration trick works with any investment that distributes cash over time.

I spend the majority of my time working on the returns of private markets investments, all those assets whose returns are usually reported in IRR (internal rate of return) terms.

IRR-producing investments embed the duration trick.

The IRR formula artificially eliminates the reinvestment risk and amplifies returns implicitly compressing them in very short duration periods. If duration is not accounted for, IRR returns create the illusion of extraordinary performance over long contractual maturities.

The reality is that it may take 12 years to realize an IRR of 20% (that has an implicit 3.2 years’ duration) – in numbers, the money allocated to such private market investment will not grow (1+20%)^12 =  8.91 x  but an honorable  (1+20%)^3.2 =  1.79 x .

Don’t get fooled by returns.
Always check the duration stick.