when to use riding yield curve strategy

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Please help, I am confused over when to use the riding the yield curve strategy. Curriculum in the Term Structure Reading says:
“If the trader doesn’t believe that the *upward sloping* yield curve will change its level and shape over an investment horizon, then buying bonds with maturity longer than the investment horizon would provide a total return greater than the return on maturity matching strategy.”
But isn’t it true that if the spot curve follows the forward curve, the total annual return is the nearest risk free spot rate? Then why would riding the curve strategy be better? Shouldn’t it be used when the projected future spot rates differ (actually lower) from the forward rates?
Sub-question is how to compute total return on this strategy.
Many thanks.
 
The sub-question: how to compute total return on this strategy:
Suppose your investment horizon is 3 years, and your strategy is to buy an 10-years bond and to sell it in 3 years.
At time t = 0, you pay P(0,10) ($) for the 10-Y bond. At time t = 3, the price of this bond will be P(0,7) (because the yield curve is supposed unchange). You will sell the bond and get P(0,7) ($).
Your total annual return: (P(0,7)/P(0,10))^(1/3) - 1
This return is higher than the r(0,3) which is equal r(0,3) = (P(0,3))^(1/3) - 1 because P(0,7).P(0,3) > P0,10) when the yield curve is upward slopping.
Return now to the main question, riding the curve strategy is better (<=> the total annual return is the farthest the risk free spot rate r(0,3)) if the yield curve is more upward slopping (which is equivalent the fact that the distance between the spot curve and forward curve is wider).
 
my understanding is when bonds have declining maturity, their yields will fall, so prices will rise.
riding the yield curve works when long term rates are higher than short term rates
 
Victoryeo1984 wrote: riding the yield curve works when long term rates are higher than short term rates
Click to expand...
This is only partly true.
Riding the yield curve works when future rates are less than those implied by today’s yield curve. This can happen if:
  • Long-term rates are higher than short-term rates (normal yield curve) and rates don’t rise to the level of implied forward rates
  • Long-term rates are the same as shot-term rates (flat yield curve) and rates fall
  • Long-term rates are less than short-term rates (inverted yield curve) and rates fall farther than the level of implied forward rates
This can be summarized easily: riding the yield curve works if bond prices rise faster than implied by the bond’s current YTM.
Rim shot.
 
I am not following just why would P(0,7)*P(0,3) > P(0,10) be true when the yield curve is upward sloping?
Here is a counterexample: if r(0,3) = 3%, r(0,7) = 3.1% and r(0,10) = 3.2%, then the total return on buy-and-hold the 3-year bond is 8.49% and the total return from rolling the curve from 10-year to 7-year bond is 7.29%, although the yield curve is upward sloping.
 
I claim the Curriculum has messed up the topic of Riding the Yield Curve. If the yield curve does not change shape over investment horizon, it has no implication for effectiveness of the riding the yield curve method.
 
I agree that if future spot rates are not as high as prescribed by the forward rates, the return will be higher. But just why is it higher than the buy and hold to maturity return? I have an example of inverse in the thread.
 
tsodoreti wrote:
I am not following just why would P(0,7)*P(0,3) > P(0,10) be true when the yield curve is upward sloping?
Here is a counterexample: if r(0,3) = 3%, r(0,7) = 3.1% and r(0,10) = 3.2%, then the total return on buy-and-hold the 3-year bond is 8.49% and the total return from rolling the curve from 10-year to 7-year bond is 7.29%, although the yield curve is upward sloping.
Click to expand...
The first question: why would P(0,7)*P(0,3) > P(0,10) be true when the yield curve is upward sloping?
You have: P(0,7)*P(0,3) = 1/(1+r(0,7))^7 * 1/(1+r(0,3))^3 > 1/(1+r(0,10))^7 * 1/(1+r(0,10))^3 = 1/(1+r(0,10))^10 = P(0,10) because r(0,3)<r(0,7)<r(0,10)
The second question: I think you miscalculated the total returns. If you ride the yield, your total return (not annual total return) is (P(0,7) / P(0,10) ) -1 = 10.66%, if you invest in 3-year bond, your total return is 9.27%.
 
tsodoreti wrote:
I claim the Curriculum has messed up the topic of Riding the Yield Curve. If the yield curve does not change shape over investment horizon, it has no implication for effectiveness of the riding the yield curve method.
Click to expand...
CFAI is too ambitious to try explain in the layman’s term the Riding the Yield Curve strategy without mathematics. Maybe CFAI does that in order to let more candidates, which aren’t very good in math, in the exams.
 
tsodoreti wrote: I claim the Curriculum has messed up the topic of Riding the Yield Curve. If the yield curve does not change shape over investment horizon, it has no implication for effectiveness of the riding the yield curve method.
Click to expand...
With all due respect, if the yield curve slopes upward and does not change, riding the yield curve produces higher returns than the initial YTM.
I mentioned this earlier.
 
First question: I agree with your proof of P(0,7)*P(0,3) > P(0,10). Still have a question about the math deduction you have demonstrated above. Will comment on it in a minute.
Second question: I have computed add-on interest, not discount interest, like you do.
 
Got it finally. Just noticed non-essential glitch: I think r(0,3) should be ((1/P(0,3))^(1/3) - 1.
Thank you!
 
I got it now. Messed up the definition of return used for calculations.Thank you!
 
Please excuse my slowness, but how do we incorporate into the above example the Forward Pricing Model? If the yield curve is UNCHANGED over the investment horizon (3 years) then current price of a forward of 7-year bond 3 years from now will be the same as the price of a 7-year bond 3 years from now. Then P(0,3)*F(3,7) = P(0,3)*P(3,7) = P(0,10), which implies that P(0,3) = P(0,10)/P(3,7), which means holding a 3-year bond to maturity provides the same return as buying a 10-year bond and selling it 3 years later as 7-year bond. Where’s the caveat?
 
Having clear notation is extremely important. In CFA Curriculum, the F(t,k) means the price of a k-maturity bond at time t. And we use P(0,k) (or P(k), or S(k) ) for the price of k-maturity bond at t = 0 (in fact, F(0,k) == P(0,k) by notation).
So, it is wrong to write P(3,7).
Depending on Unbiased Expectation Theory, we have P(0,3)*F(3,7) = P(0,10). If the (spot) curve is unchanged over the investment horizon (3 years), the spot curve in 3 year ( F(3,x) with x = 1,2,3,4,5,…) has the same value as the spot curve actual (P(0,x) with x= 1,2,3,…). We can deduce that F(3,7) = P(0,7). So, we have P(0,3)*P(0,7) = P(0,10)
 
Agree on importance of notation. Just to be precise, I think F(t,k) means the forward price of a k-maturity bond at time t. Then how do we relate the forward price of that bond to the future price of the bond? My understanding is that unchanged spot curve implies that the forward F(t,k) priced at time 0 equals the future price of underlying bond at time t. Then I conclude that rolling the yield curve brings no improvement in return.
What is that I do not understand here?
 
You must define what is forward price, what is future price.
- “forward price of a k-maturity bond at time t” means F(t,k). If the world we lives in is really predictable depending on Unbiased Expectation Theory, this forward price is determinist. Why? Because this forward price is equal, for example, F(3,7) = P(0,10)/P(0,3) and can be known at time t = 0.
Eg: When I see the spot yield curve, I found that P(0,3) =0.9, P(0,10) = 0.8. I say to you: I believe in Unbiased Expectation Theory, and in 3 year, the price of 7-maturity bond will be 0.8/0.9 = 0.88
- ”future price of a k-maturity bond at time t”, means (in this context) the “price of a k-maturity bond at time t that you guest at time t = 0”, If you don’t believe that this world is predictable or if you don’t believe on Unbiased Expectation Theory, the future price is different from the forward price.
Eg: You have an information (which I don”t have) for instant, you know a group of terrorists try to make atomic bomb, and they will have the bombs in 3 years. In 3 year, if the bombs explodes, the world (including financial world) will change, spot curve (in 3 years) will change also. You say to me that the “price of 7-maturity bond in 3 year” will be different to 0.88. This price is future price.
 
tsodoreti wrote: What does it mean “suppose yield curve does not change”?
Click to expand...
It means that the yield curve doesn’t change.
Today:
  • 1-year rate: 1.0%
  • 5-year rate: 3.0%
  • 10-year rate 4.8%
  • 20-year rate: 6.4%
One year from today:
  • 1-year rate: 1.0%
  • 5-year rate: 3.0%
  • 10-year rate 4.8%
  • 20-year rate: 6.4%
 
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