Please help me understand! I know this should be simple but I cannot seem to get it to stick so I am hoping someone has a clear way to help me grasp this, Why do they have the greatest duration (greatest interest rate risk)? Any help on tips on Fixed Income are very appreciated. Thanks in advance.
no periodic cash flows. and you get them at a big discount to par because of that. however all your cashflows if any are at maturity of the zero. so now if interest rate changes you have to pay the biggest amt?
Northern, Where are you week in Fixed Income. I have been hitting it hard for awhile now and may be able to help.
Step 1: Think of a coupon bond as a bunch of zero coupon bonds. Thus, if you get semi-annual coupons, your first zero matures in 6 months, second in a year, etc. all the way up to the big zero you get at maturity. Step 2: See that the longer the time until maturity the more interest rate sensitive the zero is. The easiest way to see that is to see that since the amount of money you have grows exponentially, a change in interest rates affects things a long time away greatly but a zero that matures tomorrow is almost completely unaffected by interest rate changes. Step 3: The interest rate sensitivity of the coupon bond is an average of the interest rate sensitivities of all those different zero coupon bonds and the big one at the end. The big one at the end is the most sensitive so the average sensitivity is surely less than the sensitivity of the big one at the end. Step 4: See that a zero coupon bond is just “that big one at the end”
Thanks for all you help guys! One more…why does the value of a call option increase when RFR is higher and the value of a put increase when RFR is lower?
I’ll try this one. Fixed income is not my strong suit either… Intrinsic value of a call = Stock price - (strike price/1+rfr) therefore higher risk free rate higher intrinsic value Intrinsic value of a put = (strike price/1+rfr) - stock price therefore higher risk free rate = lower intrinsic value
That’s aa good menmonic but it only answers the question about why does the (discounted) intrinsic value of a call option increase as RFR increases. The relationship is broader than that and is true even for OTM options. The answer to this is really in Black Scholes or nearby but the way I think about it is using Put-Call parity (assume here that S > B but you can fix this up for S < B) From Put call parity: Stock + Put = Bond + Call so Stock - Bond = Call - Put => S - B = C - P As RFR increases the bond value decreases. That causes the S - B side to increase. So that means that C - P needs to increase. It’s not a huge stretch of the imagination to say that this happens by making C increase and P decrease and some real math shows that this is exactly what happens. Put another way, if RFR increases and you want to own the stock, you probably want to put your money in a high yielding bond and have a call option. That means the call has to cost you more money.