# Annualized return

the return for 5 years on a bond is 53.87%. How will we calculate the annulaized return?

^incorrect?

I would go…[1.5387^(1/5)] - 1 = 0.09 = 9%

formula for annualized return is correct dwheats. my confusion is on the rationale behind this. if say, i multiply 9% by 5 years it comes out to be 45% which is way too less than original 53.87%. Is this the affect of compounding which I am missing here?

r(1) = 9%

r(2) = 10%

r(3) = 11%

f(1,1) = 11.01%

f(1,2) = 12.01%

based on the above data, the return of the two year zero-coupon bond over one year holding period is?

It is exactly the effect of compounding returns.

Specifically, the return is compounded annually.

PV = -1

FV = 1.5387

n = 5

PMT = 0

Solve for i = 9.0011%

Here the terms r(1), r(2) and r(3) are the spot rates and f(1,1) and f(1,2) are the one year maturity bond rate one year from now and 2 year maturity bond one year from now. Now, can you answer the question?

All this stuff’s easy.

In summary, when the yield curve slopes upward, as a bond approaches maturity or “rolls down the yield curve,” it is valued at successively lower yields and higher prices. Using this strategy, a bond can be held for a period of time as it appreciates in price and then sold before maturity to realize a higher return.

Can somebody explain this concept to me please?

What is the difference between a spot rate, coupon rate and the yield curve?

It basically means that you could earn a higher return than the bond’s YTM by selling it before it matures. Because as you go down the yield curve, the yields are lower, and you’ve essentially gained most of the YTM at some point, and holding on to the bond for longer would be less profitable than selling it for a little capital gain, and investing the proceeds in another long term bond.

Read this for a better explanation: http://www.retailinvestor.org/bondPrice.html

A spot rate (or spot curve) draws a curve of the respective spot rates for maturity dates, of theoratical zero-coupon securities (when prices are not available). Meaning that it shows the interest rate (or yield) for saving up money today, to that period (t). It’s different from the yield (or par) curve which plots the YTM as a function of time, although they are closely related since they depend on each other’s shape.

The coupon rate is simply the payment of a security as a percentage of it’s face value. A bond that pays \$60 annually for a \$1000 principal has a coupon rate of 6%.

Thank you smart. it was helpful

I wrote an article on the par curve, spot curve, and forward curve that may be of some help here: http://financialexamhelp123.com/par-curve-spot-curve-and-forward-curve/

Here the terms r(1), r(2) and r(3) are the spot rates and f(1,1) and f(1,2) are the one year maturity bond rate one year from now and 2 year maturity bond one year from now. Now, can you answer the question?

The spot rate for a bond is say 5% for 1-year maturity. What does this mean?

It means that if you’re getting a single (i.e., spot) payment one year from today, you discount it at 5% to get its present value.

Thanks magician.

You’re welcome.