Can someone explain why there is an inverse relationship between duration and market yield?
Good question… I think the misunderstanding stems from why interest rates have a inverse relationship with bond prices. The inverse relationship between bond prices and interest rates has to do with the fact that investors want to get the best return possible. If you have a zero coupon bond that trades at 960 with par value of 1000, it has a present rate of return of 1000/960 - 1 = 4.17%. If interest rates rise and you can get 10% return in the market, all things constant, why would you want to have a bond that returns 4.17% when you can get 10%? Thus, to compensate, the price of the bond will fall to 909 (to 10% yield) to attract more investors! (think about less liquidity and the fact that coupons are fixed and cannot be changed)
Now to your question, Duration is defined as a measure of price sensitivity to a 1% change in yield. Another way to look at it is that duration is the interest rate risk of a bond. the higher the yield, the less likely the price of the bond would have to change in order to attract investors, which in turn means that there is less interest rate risk (duration)!