Options and duration

CFA Level III Derivatives
#1

I’m getting hung up on the relationship between options and duration. See an example below:

Q: states that interest rates are expected to increase from the current inverse yield curve to a flat yield curve
A: “buying call options will increase effective duration while buying put options will decrease effective duration”

I get that buying put options would decrease duration, but why would buying call options increase duration? Wouldn’t they have no impact, because if rates increase, the bondholder isn’t going to call back the bond for more expensive funding?

#2

Buying call options is similar to taking a long position in a forward contract: it increases your positive exposure. If interest rates increase the value of your calls (and, therefore, your portfolio) decreases, and if interest rates decrease the value of your calls (and, therefore, your portfolio) increases.

#3

Thanks @S2000magician. If a bond investor buys call options on their fixed income investments, would they technically be short the call options? In other words, are long call options always going to be from the perspective of the bondholder?

And similarly, if somebody buys put options on their bonds (on the exam), is it assumed that the investor is always long and the bondholder is always short?

#4

Standalone options are different from embedded options; they’re like options on stock:

  • If you buy a call option, you are long the call option
  • If you sell a call option, you are short the call
  • if you buy a put option, you are long the put
  • if you sell a put option, you are short the put

Therefore, if you buy a call option, you increase the duration of your portfolio: if interest rates decrease, the value of the call option increases, and you own the call option, so the value of your portfolio increases; if interest rates increase, the value of the call decreases, so the value of your portfolio decreases. If you buy a put option, you decrease the duration of your portfolio.

BCIII

#5

That makes sense, I’m with you there. But then why wouldn’t long put options on bonds impact portfolio duration? Shouldn’t they decrease duration? See example from Kaplan below:

Q: In order to mitigate this risk, Johnson wants to decrease the duration of the portfolio to 4.5 using derivatives. (Portfolio of IG corp bonds with $500M MV, 8.5 MD, 8.0 Effective Duration, 3.5% YTM)
A: Options can be used to adjust a portfolio’s convexity: purchasing put options on bonds will decrease portfolio downside if interest rates rise, but will not impact portfolio duration.

#6

That’s an easy one: the answer’s wrong.

Buying put options decreases the portfolio’s duration.

1 Like