riding the yield curve

CFA Level II Fixed Income
#1

Just confused with the concept “riding the yield curve” and “forward price evolution”.

For riding the yield curve, if the yield curve is upward sloping, investors can buy bonds maturity longer than his investment horizon since as the bond approaches the investment horizon, it is valued using successively lower yields and therefore at successively higher price (i.e. after 1 year, you can have a capital gain). It seems that this method can earn higher return than the maturity matching strategy.

However, according to forward price evolution section, it says that if the spot rates evolve as predicted by today’s forward curve, the return on a bond over a one-year horizon is always same ie the return is the same even you purchase a bond with maturity longer than your investment horizon (e.g. 1 year) and sell it after 1 year. Does it mean that even the yield curve is rising, as long as the future spot rates evolve as predicted by today’s forward curve, the return on the bond is same no matter you purchase a bond that matches your investment horizon or not. This seems to contradict riding the curve strategy.

Anyone can point out the trick?

Thanks!

#2

Hi wtwcws,

what is important to understand is that riding the yield curve is precisely a bet against spot rates moving as predicted by forward rates which actually explains why you are confused with this seemingly contradiction.

if spot rates evolve as predicted by today’s forward rates, then YES the return over one year of bonds of any maturity is exactly the same, which is by the way the return of a one year bond.

If spot rate do not evolve as predicted by the forward curve, i.e. spot rates increase less than what is predicted by forwards or even spot rates decrease, then the strategy of riding the yield curve would generate a return over one year higher than the return on a one year bond, so traders buy a longer maturity bond even if they want to sell in one year which is riding the yield curve.

consider this example to consolidate all this:

S1 = 4%

S2 = 6%

So 1F1 (one year forward rate one year from now) = approx. 8%

Consider zero coupon bonds: the 1 year bond is valued today at 100/1.04 = $96.15

The 2 year bond is 100/(1.06)^2= $89

if you buy the one year bond, your return is naturally 4%. if you buy the 2 year bond hoping to earn 6% per year, then if the spot rate in one year is 8% (the spot moved as predicted by forward rates), your bond will be worth 100/1.08 = $92.59 at the end of year1. so your profit would be (92.59 - 89)/89 = 4%. Note how this is the same return had you invested in the 1 year bond.

Now imagine the spot rate increased by less than predicted by the forward curve. the spot rate increased to 7% at the end of the first year. the 2 year bond you purchased is worth at the end of year 1 : 100/1.07 = $93.46. if you sell it you realize (93.46-89)/89 = 5% which is more than the return on a one year bond.

and that sir, is riding the yield curve.

cheers

hope that helps.

3 Likes
#3

Do u mean riding the curve only works if the future spot rate doesn’t follow the forecasted forward curve? If future spot rate follows forecasted forward curve, then even the yield curve is rising, maturity selection strategy (I’ve buy bonds with maturity longer than investment horizon) doesn’t make us hv superior return.

thanks!

#4

Exactly! If spot rates evolve as predicted by forward rates, riding the yield curve doesn’t generate a return superior than the one year return so it’s not worth it to buy a longer maturity bond. If spot rates increase less than predicted by forward rates or even decrease, then buy a longer term bond because you’ll do a return better than the one year return. Please note that if spot rates increase even more than predicted by forward curve then buying a longer term bond will earn a return even LOWER than the one year rate. And also keep in mind our discussion assumed spot rate and forward curves were upward sloping so that’s why we were saying spot rate is expected to increase. Hope it’s clear

#5

Yes very clear! thanks a lot!

#6

Reading 35, EOC question # 38 (Solution).

When the spot curve is upward sloping and its level and shape are expected to remain constant over an investment horizon (Shire Gate Advisers’ view), buying bonds with a maturity longer than the investment horizon (i.e., riding the yield curve) will provide a total return greater than the return on a maturity-matching strategy.

Does the statement, " expected to remain constant over an investment horizon" mean that the spot rate will not evolve (increase less) as predicted by the forward curve? Appreciate any clarification.

#7

That’s exactly what it means.

Today’s spot curve:

  • 1-year rate: 2.00%
  • 2-year rate: 4.00%
  • 3-year rate: 5.00%
  • 4-year rate: 5.50%
  • 5-year rate: 5.75%

Fast forward one year: the spot curve one year from today:

  • 1-year rate: 2.00%
  • 2-year rate: 4.00%
  • 3-year rate: 5.00%
  • 4-year rate: 5.50%
  • 5-year rate: 5.75%
#8

Thanks! Somehow this trips me every time.

#9

You’re welcome.

#10

Apologies for asking a basic question, but this trips me every time.

If you have purchased a three year bond, then your return should be the YTM. Assuming an upward sloping curve s1 < YTM < s3. So your YTM should lie between 1 yr spot and 3 year spot. In that case, how can your one year return equal one year spot? Wouldnt it be less than the third year spot? What am I missing?

#11

Only if you hold it to maturity and your average reinvestment rate is the YTM.

Your 1-year return will depend on the price you paid, the value at the end of one year, and the reinvestment income on any coupon payments that year. It could be anything: less than (the original) s1, more than (the original) s3, or somewhere in between.

#12

Yup, I remember having talked on reinvestment assumption in a different post.

Could you please please please have a look at my new post on riding the yield curve. It’s unsettling.

#13

sorry. your example shows the spot rate does not evolve as forward curve suggested? would you pls provide more clarification?thx a lot!!!

#14

If the spot curve had evolved as the forward curve suggested, one year later the 1-year spot rate should have been the original 1-year forward rate beginning in 1-year; that rate is 6.0392%.

Note that one year later the 1-year spot rate isn’t 6.0392%; it’s 2.00%.

#15

“Today I want to go over techniques we use at Cuyahoga to add alpha to our active fixed-income strategies. Many of our portfolio managers like to use a portfolio management strategy called riding the yield curve. This strategy can enhance total return in two ways. First, it increases the yield of the portfolio by buying bonds with maturities longer than their investment horizon whenever the yield curve is upward sloping and expected to maintain the same level and whenever the shape and spot rates rise as predicted by forward rates. Second, even if interest rates increase unexpectedly, since the bonds roll down the yield curve, the bonds will appreciate in price.”

According to the answer sheet, Opinion 1 is correct. To me it doesn’t make any sense. Isn’t riding the yield curve a bet against spot rates following the prediction of forward rates?

#16

Thats amazing.

#17

Why is this true ? I am a little confused…
if spot rates evolve as predicted by today’s forward rates, then YES the return over one year of bonds of any maturity is exactly the same, which is by the way the return of a one year bond.

#18

I’ll illustrate it for a 2-year, zero-coupon bond; you can extrapolate from there.

Today’s price on a 2-year, zero coupon bond is:

P_0 = \frac{\$1,000}{\left(1 + s_2\right)^2} = \frac{\$1,000}{\left(1 + s_1\right)\left(1 +\ _1f_1\right)}

Suppose that spot rates evolve according to the forward curve, so that one year from today the prevailing 1-year spot rate is today’s 1-year forward rate starting in one year. Then the price of our (now 1-year bond) will be:

P_1 = \frac{\$1,000}{\left(1 + s_{1,new}\right)} = \frac{\$1,000}{\left(1 +\ _1f_1\right)}

where _1f_1 is today’s 1-year forward rate starting in one year.

The 1-year holding period return is therefore:

r_1 = \frac{P_1}{P_0} - 1 = \frac{\dfrac{\$1,000}{\left(1 +\ _1f_1\right)}}{\dfrac{\$1,000}{\left(1 + s_1\right)\left(1 +\ _1f_1\right)}} - 1
= \left[\frac{\$1,000}{\left(1 +\ _1f_1\right)}\right]\left[\dfrac{\left(1 + s_1\right)\left(1 +\ _1f_1\right)}{\$1,000}\right] - 1 = 1 + s_1 - 1 = s_1

So, the return is the original 1-year spot rate.

1 Like
#19

Thank u so much Sir…you are a genius, arent you?

#20

I have my moments.