Actuarial Outpost Spot Rates / Forward Rates - What is so special about them?
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#1
07-23-2010, 09:44 AM
 scottrf Member Join Date: May 2010 Posts: 59
Spot Rates / Forward Rates - What is so special about them?

Hi,

Can someone please explain to me what is soo cool about these rates?

From what I understand, a spot rate is essentially a yield rate for a zero coupon bond with maturity t; it is used to discount a cashflow at time t. So, if we have S1 = 8% and have \$10 at time 1, we could calculate the price of this bond by doing P = 10/(1 + S1). Whoop de do. Couldn't you do the same thing if I was told i = 8% and use that to discount at time 1 back to zero THE EXACT SAME WAY??

My view for forward rates is very similar.

So my question: What is so special about spot rates and forward rates when to me, I see them no different as plain old interest rates??

thanks!
#2
07-23-2010, 09:50 AM
 Scars Member CAS Join Date: Nov 2009 Studying for CAS Exam 5 Posts: 3,883

They are rather normal interest rates. What makes them special is when you get in to interest rate swaps. Then they serve a purpose.

For the most part, you need to understand how to transition from a spot rate to a forward rate. If you've got that down, then congratulations.

Timelines make this topic painfully obvious, and it's late in the material covered, so it can seem pretty simple.
#3
07-23-2010, 10:00 AM
 scottrf Member Join Date: May 2010 Posts: 59

What do you mean by transition from a spot rate to a forward rate?
#4
07-23-2010, 10:12 AM
 Car'a'carn Member SOA Join Date: Jul 2004 Location: The Waste Posts: 4,678

Quote:
 Originally Posted by scottrf What do you mean by transition from a spot rate to a forward rate?

Spot rates are current rates. Forward rates are rates which start at some point in the future. There must be a relation between them to avoid arbitrage.
#5
07-23-2010, 10:15 AM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 26,458

Quote:
 Originally Posted by scottrf Hi, Can someone please explain to me what is soo cool about these rates? From what I understand, a spot rate is essentially a yield rate for a zero coupon bond with maturity t; it is used to discount a cashflow at time t. So, if we have S1 = 8% and have \$10 at time 1, we could calculate the price of this bond by doing P = 10/(1 + S1). Whoop de do. Couldn't you do the same thing if I was told i = 8% and use that to discount at time 1 back to zero THE EXACT SAME WAY?? My view for forward rates is very similar. So my question: What is so special about spot rates and forward rates when to me, I see them no different as plain old interest rates?? thanks!
They are normal interest rates. They are an efficient way of describing interest rates that vary over time to maturity, which is very important in the real world.

i = 8% is very simple, but how to you say all of these with interest rates: invest \$100 in a one-year zero-coupon bond today, get back \$108 at maturity. Invest \$100 in a two-year zero-coupon bond today, get back \$120 at maturity. Commit today to investing \$100 in a one-year zero-coupon bond three years from now, get back \$109 at maturity. A table of spot rates gives you the first two directly (and would let you calculate the third). A table of forward rates gives you the third directly.

No single value of i does that.

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