Bond YTM Question during Interview
I got this question during a finance interview with a top prop shop. I dont think I answered correctly. Can someone help me figure out the correct answer?
What is the 1-year holding period return of a 30 year US Treasury if it is currently selling at par ($100) with a 7% coupon and the Yield to Maturity a year from now is 11%?
(Assume entire 7% coupon is paid at the end of year rather than semianually)
Loss of $28
Alright, so lets do it this way:
1) Find the Price of the Bond at t=1 We know Price and Yield have an inverse relationship, therefore intuitively the price should be lower at t=1 since yield increased to 11% (since its selling at par, current YTM is 7%).
Solving for price you get 65.40... if you want an estimate you can use Current Yield
CY= C/P 11%=7/P P= 63.6
Remember for discount bonds CY is greater than YTM and for premium bonds CY is less than YTM.
2) Now we can solve for HPY
HPY= (7+65.40-100)/100 = -27.6%
I believe this is how it should be done.
I'm sorry but how did you get 65.40?
You could use a financial calculator or excel ( =PV(11%,29,7,100) ):
11% YTM = Yield 29 = Periods Remaining 7 = Coupon 100 = Face Value
=65.40
Like I said, you could use Current Yield to estimate it, since the number of periods is large, it should be relatively close.
Revsly has a pretty good answer, although in reality the US Treasury is paying you semi-annual interest.
FV= 100 N= 58 (instead of 29 years, you have 58 six month time periods) PMT = 3.5 (you receive half your coupon every 6 months) I = 5.5 (divide the annual YTM in half to account for 6 month time period)
PV = 65.26
HPY= (7+65.26-100)/100 = -27.74%
You need to include interest from reinvestment of coupons
there is a formula which gives you price from yield...if you're familiar with geometric series (particularly sums of geometric series), you can derive the formula....the price is basically the sum 7/(1+11%)^1 +.....+107/(1+11%)^30....which is a geometric series
yes, thats called the fucking annuity formula which every high school kid knows, for a semi-annual compounding bond of maturity t, yield r, coupon C, notional N the price is:
P=(C/r)*(1-(1/(1+r/2)^2t))+N/(1+r/2)^2t=65.27 in this example
The formula I know is
Annuity of a bond = perpetuity(1-perpetuity(discounted to the last period) + principle(discounted to last period)
Bond PV = 7/0.11(1-1/0.11(1.11)^58)) + 100/1.11^58 = $62.51 or 62.511%
I could be wrong but don't think you need to divide the yield to maturity to 5.5% if you have doubled the discounting period.
cost of debt- YTM vs Current Yield (Originally Posted: 02/28/2010)
During my BX superday a few weeks ago, one of the interviewers grilled me on using current yield vs YTM for the cost of debt.
This is something that I've been confused about for a while. My professor told me use YTM but some bankers told me they use the current yield, am I missing something here? What do you guys use?
-Thanks
IRL, we use indicative spreads from the DCM group.
From a theoretical standpoint, if you have to choose between the YTM and the current yield, always use YTM since it accounts for the gain or loss that will occur when the par value is repaid. The current yield is just an approximation of the YTM.
^^^^ Right on Righton.
Modelling YTM (Originally Posted: 01/07/2011)
I am preparing for an upcoming interview for a credit group and was told they can sometimes ask people to calculate YTM in excel. The exact quote was "they may ask you to calculate YTM assuming you get refid in two or three years time.
What is the best way to do this? Excel has a few functions, I usually use the RATE function but I know the YIELD function exists. Are their others? If not, between RATE and YIELD, what is better / would provide the most accurate answer.
Also, I don't know what data they give you but presume it is in -price acquisition date coupon call data estimated re-fi date
Project the cash flows with the dates and use XIRR. Technically getting refi'd out would be a yield to call, rather than a YTM, not sure why they would call it YTM.
You are right,, this probably seems easier than relying on a formula.
How to find YTM if given Face Value, Market Value, and Interst rate? (Originally Posted: 01/20/2013)
Friend got asked this in an interview.
How do I approximate YTM?
Scenario:
FV = $1000 Mrkt Value = $900 Annual Coupon = 5% Maturity = 5 years
google financial calculator
900 = 50(1-(1+YTM)^-5)/YTM + 1000(1+YTM)^-5, solve for YTM, which you can't do algebraically. I assumed you wanted annual coupons, but bonds are semiannual, so it would be 25 not 50 and 10 not 5 in that case.
For a semi-annual coupon, the iterative process such as Newton-Raphson method helps find the YTM
You would have to solve for the interest rate in the bond price formula, it will also require knowing the 1st order derivative of the bond price
f(i) = 1000 + -900 * (1+i)^10 + 25 [(1+i)^10 - 1]/i
f'(i) = 10 * -900 * (1+i)^9 + 25 * (10 i (1 + i)^9 - (1 + i)^10 + 1) / (i^2)
i = 0.1 f(i) = -935.9326 f'(i) = -19311.0161 i1 = 0.1 - -935.9326/-19311.0161 = 0.051533746738395 Error Bound = 0.051533746738395 - 0.1 = 0.048466 > 0.000001
i1 = 0.051533746738395 f(i1) = -170.853 f'(i1) = -12666.9086 i2 = 0.051533746738395 - -170.853/-12666.9086 = 0.03804560833436 Error Bound = 0.03804560833436 - 0.051533746738395 = 0.013488 > 0.000001
i2 = 0.03804560833436 f(i2) = -9.9487 f'(i2) = -11217.2599 i3 = 0.03804560833436 - -9.9487/-11217.2599 = 0.037158700659625 Error Bound = 0.037158700659625 - 0.03804560833436 = 0.000887 > 0.000001
i3 = 0.037158700659625 f(i3) = -0.04 f'(i3) = -11127.2132 i4 = 0.037158700659625 - -0.04/-11127.2132 = 0.037155107831769 Error Bound = 0.037155107831769 - 0.037158700659625 = 4.0E-6 > 0.000001
i4 = 0.037155107831769 f(i4) = -0 f'(i4) = -11126.8497 i5 = 0.037155107831769 - -0/-11126.8497 = 0.037155107773083 Error Bound = 0.037155107773083 - 0.037155107831769 = 0 0.000001
Periodic YTM = 3.72% Nominal YTM = 7.43% Annual effective yield = 7.57%
Bro...seriously? Come on man...
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