I want to draw efficient frontier for a T/Bills and T/Bonds portfolio to identify the best asset allocation(tenor allocation). The credit rating for all T/Bills and T/Bonds are same since the issuer is same. I have a question on how to calculate expected return and variance. Suppose I am dividing my portfolio based on time to maturity as 1Y,2Y,3Y & beyond 3Y (Y denotes years) to sub portfolios. To calculate the expected return for I Year T/Bonds sub portfolio,can I use the formula, expected return = (bond Face Value-Purchase price)/purchase price and then multiplying with weightages. My issue is how to calculate the variances of 1Y,2Y,3Y and 3Y beyond sub portfolios separately? Or is there any other way to identify tenor allocation or bond portfolio analysis techniques?
I would probably use YTM for each maturity to gather the expected return
Return measure YTM as yayyywork says looks fine.
About variance, why don’t you use effective duration? Or at least modified duration if no bond contains any option (call, put, conversion, etc). What is your investment time horizon? Be careful with bonds with a tenor higher than your investment horizon, you run a price volatility risk there.
If all bonds has the same credit rating, then the risk comes from interest risk and reinvestment risk and not much from credit risk. Again, set clear the investment horizon. Just an advice.
Thank you Yayyywork and Harrogath for your comments,
Yes I agree,YTM is a better option to calculate the expected return.
Harrogath, Your insights are really valuable,Can I take the weighted avg Modified durations as variance for sub tenor portfolios?
investment horizon is a bit of an issue since Bonds are funded by short term funds. Reinvestment risk too needs to be calcuted.
Thank you
You mean weighted avg modified duration for group of bonds? I though you were trying to discriminate between single bonds.
Depending of your investment strategy you will need to calculate the relevant measures. Sorry for not being more help.
Yes, I mean weighted avg modified duration for group of bonds. If this is to discriminate between single bonds then mod duration is highest in the longer tenor bond and lowest in shorter tenor bond mostly. Because Mod duration equals macauly dur/(1+r). Excel calculations are without convexcity adjustment.Portfolio variance/return of n assets can be calculated by matrix multiplication in excel or using Mathlab. Thank you for your support. any suggestions are also welcome since this is not finalised yet.