I’m trying to create a monthly and quarterly return stream based off of daily published LIBOR Rates to use as a risk-free index. I’m specifically looking at the 3 month LIBOR, but am interested in understanding how this would apply to all LIBOR borrowing periods.
I would imagine there’s an industry standard way of doing this, but I’m having trouble googling or thinking through a solution that I’m confident in. The first thing that comes to mind is that my monthly values should compound up to my quarterly value, so my thought is that I really only need to focus on a monthly return stream. How should I apply the published rate to come up with this monthly return stream though?
The simplest solution is maybe to divide the published rate at the beginning of the month by 12 to get the monthly equivalent and assume that that rate is applied throughout the month. I may be overthinking this, but this is both missing information about the rate intra-month (which may be fine) and there seems to be a disconnect with the borrowing period.
To capture information on intra-month rates (I realize this may not make sense), I could apply the daily rate associated with the published annual rate for each day in the month. This would involve applying the last published rate for days that it isn’t published (e.g. weekends) and compounding this up into a monthly return. This gets a little messy for non-GBP (I’d want to have a method for all currencies) rates due to the 360 day count convention. Again, the borrowing period disconnect is troubling too.
The last method that comes to mind is rolling over a 3 month contract, which makes the most intuitive sense to me as it seems most applicable to how this may be accomplished in the real world. Would I need the 2 month rate to “close out” the prior month’s contract? Any thoughts on the exact mechanics of this if this is the best option?
Anyway, I’d be very appreciative of any feedback that anyone may have on this. My goal is to have the most accurate and theoretically correct return stream that I can, so complexity isn’t a problem if it’s the right way to do it.
Are you talking about getting the spot rates and using linear interpolation to draw the LIBOR curve? Then the function can reference that table to get the right spot rate for each future period (whether its days, months, etc).
Thank you for the reply rawraw. I’m not trying to do any linear interpolation to estimate spot rates between the published borrowing periods, I’m actually trying to do something much simpler and am probably overthinking it.
All that I’m trying to do is create a monthly return stream based off of the 3 month LIBOR published rate. I could then calculate the annualized return of this ‘risk free asset’ over any time frame that I wanted for use as a risk-free rate for Sharpe Ratio calculations, etc.
I just can’t think through or find a methodology that I’m comfortable with, and was curious if anyone had any thoughts or suggestions.
I don’t understand, I guess. So you want to engage in 3 month investments every 3 months and the relevant risk free rate is 3 month libor? And then you want to compare how you are doing to the risk free rate?
Suppose you had a laddered portfolio of 3 month LIBOR notes. Every month, the following things happen:
You receive one month’s worth of interest on last month’s capital, at the rate that applied at the beginning of the month.
One third of your portfolio matures and can get rolled into a new 90d LIBOR note
The other 2/3 of your portfolio gains or loses capital value due to any interest rate changes. The durations are approximately 3/24ths ( 1/2 * (1/12 + 2/12) ) and 5/24ths ( 1/2 * (2/12 + 3/12) ) respectively, though you could also use the 60d and 30d LIBOR rates if you have them.
So your portfolio growth is a combination of the interest received and the change in capital value. Assuming there isn’t a huge change in LIBOR rates, you can approximate by assuming that you reinvest the total in equal thirds at whatever the rate is today.
Take a look at how that total portfolio behaves. Compute its monthly returns by comparing the portfolio’s total value at the end of each month.
There’s another way you can do this, which is to keep track of rolling periods. You have a laddered portfolio of 90d, 60d, and 30d bills, and each month you grow the value of each third by 1/12 of the annual rate that they were purchased at. Every month, you can assume that the value of the portion that had 30d left gets rolled over to whatever the new rate is. If you want to be extra finicky, you can figure out how much of the 60d and 90d bills you have to sell or buy to rebalance, but personally I could never be bothered. Then go and compute the monthly returns by how the value of that portfolio grows.
If you are doing this with real money, then you have transaction costs in there too, so it may make more sense just to roll over whatever has matured plus any interest you have accumulated into new 90d bills.