Hi guys. Please can someone explain the rationale behind below statement -
‘the higher the level of interest rates, the lower the price volatility of a bond to changes in interest rates’
i am probably missing out on a very generic logic here, pls help
thanks
The statement is strangely worded, but if I read it correctly, it is asking how the price changes in response to a change in interest rates at various levels.
The price/yield curve for a bond without an embedded call option has a negative slope but is convex (i.e. the second derivative is positive). So, the slope becomes less negative as the yield increases.
In other words, the duration gets smaller as the yield increases. So, (for example) a 100 bp change in interest rates will result in a bigger % change in price when market rates are at 5% than it will when rates are at 10%.
All it says is that as YTM goes up, duration goes down.