# Riding the yield curve, anybody?

Hey guys,

Could someone explain to me what does this mean and what are the main take aways?

And also, rolling down the yield curve…

Consider an upward sloping yield curve, i.e. higher yield for longer maturity. Consider a 30 year government bond. You purchase it for \$X. Five years later, the bond has 25 years to go till maturity, which is less than the original 30 years, which implies a lower YTM. Lower YTM increases the bond price. You sell the bond for a profit. Key takeaways are: a. Your investment horizon is less than the maturity (5 years compared to 30 years) b. Yield curve is upward sloping That’s how I understand it.

Imagine there are some zero coupon bonds on offer and we have some different yield curve shapes. Your investment time horizon is 5 yrs

This only works if the shape of the yield curve doesn’t change (or changes little enough that you still make a profit… but let’s not complicate things)

Scenario 1: Crazy steep yield curve

the 30y ZCB yields 10% (price: 5.73; n=30,I/Y=10,PMT=0,FV=-1) the 25y ZCB yields 5% (price: 29.53; n=25,I/Y=5,PMT=0,FV=-1) the 10y ZCB yields 4% (price: 67.56; n=10,I/Y=4,PMT=0,FV=-1) the 5y ZCB yields 2% (price: 90.57; n=5,I/Y=2,PMT=0,FV=-1)

If you buy the 30y and sell it in 5 years time, you will have made ((29.53/5.73)-1)=415.36% profit If you buy the 10y and sell it in 5 years time, you will have made ((90.57/67.56)-1)=34.05% profit If you buy the 5y and hold to maturity, you will have made ((100/90.57)-1)=10.41% profit

Scenario 2: Not so steep

the 30y ZCB yields 5% (price: 23.14) the 25y ZCB yields 4% (price: 37.51) the 10y ZCB yields 3% (price: 74.41) the 5y ZCB yields 2% (price: 90.57)

If you buy the 30y and sell it in 5 years time, you will have made 62.1% If you buy the 10y and sell it in 5 years time, you will have made 21.72% If you buy the 5y and hold to maturity, you will have made 10.41%

(as curve is not so steep, you still make money “riding the curve” but less than under scenario 1.

Scenario 3: Flat

the 30y ZCB yields 5% (price: 23.14) the 25y ZCB yields 5% (price: 29.53) the 10y ZCB yields 5% (price: 61.39) the 5y ZCB yields 5% (price: 78.35)

If you buy the 30y and sell it in 5 years time, you will have made 27.63% If you buy the 10y and sell it in 5 years time, you will have made 27.63% If you buy the 5y and hold to maturity, you will have made 27.63%

(notice this helps understand why 1yr returns = same for any maturity if FORWARDS don’t change, as a flat spot curve implies non-changing forward curve…)

Scenario 4: Inverted

the 30y ZCB yields 2% (price: 55.21) the 25y ZCB yields 3% (price: 47.76) the 10y ZCB yields 4% (price: 67.56) the 5y ZCB yields 5% (price: 78.35)

If you buy the 30y and sell it in 5 years time, you will have made -13.5% If you buy the 10y and sell it in 5 years time, you will have made 15.97% If you buy the 5y and hold to maturity, you will have made 27.63%

(as curve is inverted you would lose money by investing further out)

Because your principal from the ZCB is being discounted at lower rates as time goes on in scenarios 1&2, you benefit from an upward sloping yield curve by investing at a higher YTM. Vice versa for scenario 4.

Good stuff @burberryjam with the numbers!

you guys are awesome

Great, but is this the same as riding the yield curve strategy? What’s the difference here anyone?

Riding the yield curve and rolling down the yield curve are synonymous.