Volatility term structure


The CFAI text (Reading 37) stated this in regards to checking whether a bond valuation system is adequate:

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Why does the volatility term structure have to slope downward?


I am interested to know this too.

Why does the shorter maturity rates have higher vol then longer maturity? For example 6 month Vs 20 year. Schweser says short rate vol comes from montery policy wheras long rates come from economic shifts and inflation. As there is more uncertainity over what inflation will be in say 20 years does this not imply more volatility? THerefore an upward sloping curve?

Hi Rex,

In the context you’re mentioning, I think I understand why short term vol is higher whereas long term vol is lower. As you said, short term vol is affected by monetary policy, whereas long term vol is influenced by the real economy & inflation. I believe that monetary policy is more variable than the real economy & inflation, which are longer-term factors that concern growth of the economy, changes in price levels, and other factors that unfold over longer periods of time.

Therefore, as monetary policy is more variable than the real economy & inflation, it would result in short term vol being higher than long term vol.

Hope that clears things up.

What I don’t understand, however, as in my initial question, is how short-term volatilities imply longer-term volatilities. I also don’t understand why short-term volatilities should be lower than longer-term volatilities in order for the interest rate process (whatever the interest rate process means) to be stable.

Foreseeing the long-term future is harder than the near future. When the market sets the long-term interest rates, it also sets, say, 3 scenarios for the long term: Bad, Normal and Good, and their respective probability of occurrence. Each scenario has its own interest rate, so blended is the market equilibrium rate for long-term investments. However, for the short term (near future), the market sets, say, 24 scenarios, or 32, or 64, or 100…for the economy; from “Armageddon” scenario to “I Touched The Heavens” scenario. So the volatility of short-term interest rates is much higher.

See the economy as a dynamic machine that approximates to the future day by day. The new data today may change the projections of the long term, so the long-term volatility of interest rates implies the short-term volatility of interest rates. In simple words, the future is a function of the present: Future = f(present).

The explanation of monetary policy and real economy performance is really accurate. The output is practically fixed and predictable and the tendency is upwards (world real GDP has risen since first records), so the long-term is low volatile. However, the short-term (that builds the future day by day) has proved to be much more volatile, hence the interest rates and the other prices of the economy.

Hope this helps.

Thanks Harrogath for the detailed explanation.