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Computation of the Normal Yield Curve. 0 comments
Plea for a New World Economic Order.
Chapter I, Paragraph1:
Computation of the Normal Yield Curve.
This development contrasts with most experience, which suggests that, other things being equal, increasing shortterm interest rates are normally accompaniedby a rise in longerterm yields.
The simple mathematics of the yield curve governs the relationship between short and longterm interest rates.Tenyear yields, for example, can be thought of as an average of ten consecutive oneyear forward rates.
In the current episode, however, the moredistant forward rates declined at the same time that shortterm rates were rising. Indeed, the tenthyear tranche, which yielded 61/2 percent last June,is now at about 51/4 percent. During the same period, comparable real forward rates derived from quotes on Treasury inflationindexed debt fell significantly as well,suggesting that only a portion of the decline in nominal forward rates in distant tranches is attributable to a drop in longterm inflation expectations"
Chairman Alan Greenspan
Federal Reserve Board's SemiAnnual Monetary Policy Report to the Congress.
Before the Committee on Financial Services, U.S. House of Representatives.
July 20, 2005
Abstract:
I am going to show that the normal yield curve is a function of the short term rates and of the volatility of interest rates. The obvious consequence is that you can't determine shortterm rates (monetary policy) without taking in account longterm rates.
We are going to use a new model of longterm interest rate, which is rarely used: longterm rates as a geometric average of options on shortterm rates. In fact
Interest rates as Options:
Fischer Sheffey Black first introduced this notion. It was his last work and was published after his death.
Interest Rate as Options, Fischer Sheffey Black, Journal of Finance, Vol. 50 No. 5, December 1995.
I propose a different use of the option point of view.
Forward Rates as Options:
R [t+ T] = Call [R[t], Vol R (t, t+T),0]
Where R [t] is the forward interest rate (annualized or continuouly compounded) for the period starting at t
Vol R (t, t + T) is the implied volatility of the interest for the period [t, t+T].
0 is the strike of the call option: obviously interest rates can't be negative.
The difference between R [t + T] and R[t] is hence the time value of an option.
The slope of the difference between two forward rates is hence the time value of an option.
The longterm rate being the composition of forward rates, the slope of the yield curve is hence a positive function of the time value of an option.
Locally if the option is undervalued the Market prefers the underlying asset rather than the option.
It prefers shorterterm maturity rather than longer term maturity.
This preference is local.
We derive from that our definition of normal yield curve steep yield curve and inverted yield curve.
These notions are global we will take them as approximate extensions of the local notions we have explored. We will hence be making an approximation: "I prefer to be roughly right than exactly wrong."
Normal Yield Curve:
A yield curve is normal if the options are fairly valued. There is Market indifference between the asset and the option. There is Market indifference between assets of different maturities.
Because time value of an option grows with its maturity, the normal yield curve is upward sloping. Because the time value of a call decrease as the value of the asset moves away from the strike price, the curve is convex.
The higher the implied volatility of interest rates the steeper the normal yield curve.
Inverted Yield Curve:
A yield curve is inverted if the option is undervalued. Longterm rates are too low compared to shortterm rates. Because of the inverse relationship between present value and interest rate, there is Market preference for the shortterm asset over asset of longer maturities. It is what Keynes termed liquidity preference.
Our definition says that a yield curve may be upward sloping and inverted. A flat yield curve is necessarily inverted because the time value of an option is always superior to zero (unless of course volatility is zero!!!).
Steep Yield Curve:
A yield curve is steep if the option is overvalued. Longterm rates are too high compared with shortterm rates. There is Market preference for asset of longer maturity over asset of shorter maturities.
Arbitrage:
Because we saw that the yield curve can stay inverted for quite an extended period of time the arbitrage of the yield curve is not straight forward (punt intended.) However it is a risk free arbitrage which can be done by buying the spread longterm yield / shortterm yield and shorting a complicated option on interest rates. I will let the Quants of the various hedge funds do that for us. It is their job to maximize the present value of future cash flaws.
All of This Stays True Until the Poor Becomes Richer Relatively to the Rich.
Extreme Economic Conditions Call for Radical Solutions.
The Controversial Innovation Since John Maynard Keynes and Milton Friedman.
It is Vital That, When the Crash Comes, we Restore as Fast as Possible the Economy by Implementing our Plausible Alternative Solution as to Minimalize the Economic Sufferings of the People. To That Order I am Building Redundant Social Networks. Please Connect With Me!
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