‘While effective duration of straight bonds is relatively unaffected by changes in interest rates, an increase (decrease) in rates would decrease the effective duration of a putable (callable) bond.’

It did not offer any explanation so I’m still pretty confused here. What is the intuition behind this statement?

In the simplest sense, if you hold a bond with an embedded put option and market interest rates subsequently rise, all else equal you would be more likely to exercise the put and invest in a bond that will offer a higher rate of return. Therefore the effective duration of a putable bond decreases when market interest rates increase.

In the case of a callable bond, if market interest rates decrease the issuer would be able to decrease their cost of funding by issuing debt to investors with a lower rate of return. Therefore the call option is more likely to be exercised when interest rates decrease, and the effective duration of the callable bond will decrease.

Their statement about putable bonds is correct, while their statement about callable bonds is, at best, half correct.

I suggest that you draw the price/yield curve for a callable bond, and for a putable bond. While it is not true that the effective duration is the (negative of the) slope of the price/yield curve, it is very similar to the (negative of the) slope of the price/yield curve, and imagining those slopes as the effective duration will help you to understand that sentence very quickly.

Effective duration = % change in price of the bond for 1% change in yield.

When the bond price is near the call (put) price (or already in-the-money), a decrease (increase) in rates would not change the value of the bond (much) as the call (put) price is fixed. This relative insensitivity is the intuition behind the reduction in effective duration (relative to a straight bond).