shape of yield curve

Is it correct to think of the yield curve as being determined by a series of future short term interest rates? Or alternatively is it possible to tell what the market is pricing in for the federal funds rate in the future just from the yield curve? how would it work mathematically if its possible?

 
Best Response

You can "bootstrap" the curve of future spot rates using the yield curve. It involves assuming that each on the run treasury is issued at par and using earlier rates in the curve to find the last rate in the curve, (ie using the 1 yr and 2 yr rate and 3 yr treasury price to find the year 3 rate, discounting the first two coupon payments by their respective rate, (assuming an annual pay bond is easiest for this example)) Something similar can be used to find forward rates. The idea is to make an investor indifferent b/w invetsing in a 1 yr bond now and a 1 yr bond in the future, OR investing in a 2 yr bond now. Knowing the 2 yr rate, and hte 1 yr rate, and using simply division, you can find the 1 yr rate, 1 yr from now. Pure expectations theory states that longer maturity rates are what short term rates are expected to be in the future. This is opposed to the liquidity preference theory and the preferred habitiat theory that are both "biased" theories are are generally thought to be more applicable.

It is worth noting that the spot rate curve, is not equivalent to the yeild curve, and in an upward sloping yield curve environment, will be above the yield curve. Generally, bonds are priced off hte spot curve, not the yield curve.

 

Money Markets by Marcia Stigum, the Eurodollar Futures & Options Handbook by Burghardt and Trading STIR Futures by Aikin are all books that I've read recently that touch on the subject. That being said, they don't devote much time to bootstrapping. Unfortunately I'm not totally sure what else to recommend. This (http://www.amazon.com/Analysing-Interpreting-Yield-Curve-Finance/dp/047…) looks like what you're looking for but I haven't read it and the reviews seem all over the place.

 

why are you studying this? i trade bonds and i can tell you that no one outside of 1st year analysts really get into the nuts and bolts of it. if you're doing this for interviews, the knowledge on this thread is conceptually enough.

 

also, if you find forward rates by using the yield curve, is the result the exact expectation of short term rates over that period? is it ok that the forward rates increase fairly linearly with time? isn't that kind of unrealistic if they're supposed to be projections of short term interest rates in the future?

 

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Its been a while since I was in school and I dont work in DCM but...

The yield curve is a depiction of the premium/discount the market places on US Treasury securities of varying maturities. Under normal economic conditions you see an inclined yield, this basically means that the mkt demands higher returns on treasuries with longer maturities... reason being the increased risk associated with securities of longer maturity(default, int rate).

1- 3-mon +.06% 10-yr +.02 indicates that the mkt has changed its perception of risk on these securities... specifically, mkt perceives an increase in risk on short-term maturities and a slighter increase in risk on longer-term maturities; as a result mkt wants to be compensated accordingly. Simplified, this inverts the yield curve... an inverted yield curve is when the mkt demands a higher return in the short-term and lower in the long-term.... this usually indicates a pending recession.

2- its because the FED rate has dropped repeatedly starting in Sept 07. As for what it means... umm... maybe someone else can answer that since theres alot of different dimensions to it. Basically FED dropped rates to cushion credit/liquidity crunch.

 

good explanations Elan. So does it mean that on a daily basis, an increase in yield means that the market is viewing the economy in a more negative light- less demand drives down the price and increases in yield?

Yet when we look at the yield curve from a year ago. Today's yield curve should be higher because the market looks worst now than it did a year ago. The only reason why the yield curve is higher today than a year ago is because the Fed artificially intervened by lowering the curve?

 

Jason, in fact the opposite is true. As I'm sure you know, yields on a security compress when people are bidding up the price of the security, and expand when people are selling the security. People use treasuries as a safe harbour for cash when other investments (ex. equity) begin to look less attactive. As the economy looks choppy, money flows out of equities and into treasuries, and yields compress. When equity markets start looking more attractive, the opposite will occur. That's why you'll see yields on treasuries compress noticably on a day when bad economic news is released, or if the equity markets have a terrible day.

As far as the shape of the yield curve at any given time, that's a different question and I think elan covers about as much as I could.

 

Can generally be taken to interpret what the market's expectations are for future inflation and reinvestment risk. Take for instance an inverted yield curve. Now, we have ST securities yielding more than long term. Remember, in theory, the curve is a reflection of expectations tomorrow based on yields today. So in the case of our inverted yield curve, we could say the market expects long term inflation to be low, ST to be higher, etc. Think about each risk of the bond based on its time to maturity. For instance, a high or low curve says nothing about reinvestment risk on a 30 day bond, because there is essentially none. But, for a long term bond...well, you got it. Easy stuffages.

 

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