Question

Can someone please help me, I am trying to find Face Value of Bond (FV), Effective Annual Interest Rate (EAR), Yield to Maturity (YTM) if held to maturity and Total Return for Investment portfolio for the 6 month treasury below. Please show your work so that I can try to grasp this. Thank you

6-month Treasury Bill (GB6:GOV)

Face Value of Bond (FV) $        ?  

Price $ 1.54

Yield 1.58%

Asset Category: U.S. Treasury and U.S. Agency Securities

Asset Classification" Cash Equivalent

Issue Date 11/14/2019

Maturity Date 5/14/2020 182

Money Market Instrument Identifier: U.S. Treasury CUSIP 912796TV1 Effective Annual Interest Rate (EAR) ?

Yield to Maturity (YTM) if held to maturity ? Current Price of Bond (PV) $ 1,125,000

Total Return for Investment portfolio

Answer 1

1) Price given = $1.54

use:- Price=F.V/((1+r/x)^n) where x= number of times you would compound in a year(here 2, as 6 month treasury bill) , r= annual interest rate, n= number of periods you would compound to(n=1 here as maturity is of 6 months only)

So, 1.54= F.V/((1+0.0158/2)^1 )=> F.V= 1.552166

2)Assuming that you have to calculate the EAR for the same rate(r) mentioned in 1st part, use:-

EAR= (1+ r/n)^n -1; where n is the number of time periods you are dividing the annual interest rate (r) by and hence compounding again to get the EAR.

So, EAR=(1+0.0158/2)^2-1=0.01586241

3rd and 4th part aren't clear exactly. Please specify the F.V for which YTM has to be calculated and what instruments are present in your portfolio exactly.