Risk free rate to use

I’m working in ER for a well established MM private bank. The thing is almost all of the analysts use the one year risk free rate in their valuations. I’ve also seen this in asset managment at another BB in the past while interning. Their reasoning is that research reports are aimed for investors who plan on holding securities for the short-term to benefit the change in price in the next year, and not for 5 to 10 years. I’ve tried arguing that this isn’t proper practice, and the discount rates must match the cashflows used. So the first period uses the 1yr RFR, second period uses the 2yr RFR…etc. While most institutions just use the 10 or 20 RFR.

Am I wrong in my assumptions? If not, how do I explain it?

In bond work, you do look at risk free spot rates and compute spreads like this.

For equities work, there’s so much noise in the earnings projections that going through all that effort to be precise on the RFR spot rates is a bit like trying to measure your body weight to the gram. You can do it, but the next time you take a drink, eat a meal, spit, sweat, come, or drop a deuce, the figure is going to be wrong. Getting to the nearest pound or kilogram is perfectly sufficient, given the fluctuations of everything else.

In general, you want to tune your RFR rate to the length of your investment horizon. For an asset allocation framework, typically you’ll use something like a 10y Treasury rate, figuring it’s an approximate average of all of the intervening rates, and tells you more or less what you’d get if you just sat on your money for that length of time.

However, if you have an active strategy, it’s not uncommon to tune the RFR to the rebalancing period, though that really only makes sense if holding cash actually is a realistic option for your investors to do. If you’re just going to reissue a report in a year with new analysis, using a 1 year rate is not unreasonable, however, it’s pretty obvious that some people like to use the 1 year or even 90d rate because it makes their sharpe ratios look better while the fed is pursuing ZIRP. In more normal times, the curve is not this steep, so the decision has less material effect on performance ratios.

I’m not in the US, so the ZIRP doesn’t apply where I live.

In any case, if you’re doing a DCF, wouldn’t you be overvaluing the asset if you use the short term interest rate for ALL the periods in the future? The gradual laddering of discount rates starting from the first period and a final big bump on terminal value should relfect both, the time value of money, and the uncertianity of future E/CF. So even though the investment horizon is only for one year, the asset in question is a going concern, and deriving their present value today needs to be consistent, irregardless of the investor’s behaviour. After all, the whole concept behind DCFs is deriving the intrinsic value, and matching them with the current market price?

Yes, but the differences are going to be slight unless the yield curve is either very steep or very inverted.

But more importantly, it’s a lot of work in a not-so-trivial calculation to add a tiny bit of precision to something that is going to be overwhelmed by (except in unusual situations like ZIRP) much larger random factors and uncertainties in the revenues and profit margins anyway. If your process applies anything like a margin of safety, it’s just not going to make a difference in a decision to pull the trigger.

If you find that the “intrinsic value” is $0.02 less than the price, you’re not likely to lever up and say “Go baby, go!” because you know that there may be lots of unexpected things happening to the underlying business.

In fixed income, you know (at least with straight bonds and simple amortizations) how much is going to be paid, and when, so all of a sudden those big uncertainties disappear. And then, yes, the term structure of interest rates suddenly becomes important. But look at credit spreads, and how much they affect actual bond prices. Then compare those price changes with the fluctuations you get in equities prices, and then you’ll see why people don’t bother with using RFR term structure in their equity DCFs.

And how do you come down with a terminal value if you aren’t going to assume a constant RFR after some point in time. A multiple?? The justifiable change with the RFR. You can’t use a gordon growth model to produce a terminal value without a constant RFR. What year are you going to use? 5? 30? 50? Many stocks have a duration of 50, so maybe the 50y that’s the right one to use. Wait… are there even 50y bonds out there to use?? (not in most countries)

But if you assume that your investor is going to sell the stock in 5 years, then maybe you should use a multiple that reflects the 5y RFR. It just opens so many questions that depend on the investor’s situation that most people will simply say “the average RFR over the long term is (or has been) 2.5 expected inflation + 3% real GDP growth rate (for example). We’ll use that.”

It only makes sense to let the RFR drive your valuation once you’ve figured out what the equity risk premium ought to be. Get that number nailed down to the right number of basis points, and then you can start to sweat over whether you should be using the term structure or an estimated average.

Finally, the right RFR is tuned to the investor’s holding period. If you are going to reevaluate in a month and potentially exit the investment at that time, your holding period is actually 30 days, which would suggest that something like a LIBOR 30d rate is more appropriate than a 30y bond.

You could then ask, “But what if I keep holding this investment for 30 day period after 30 day period for 30 years. Doesn’t that mean I should have used a 30 year rate after all?”

And the answer to that is: It wouldn’t be wrong to use the 30 year bond rate if you know that that’s what you end up doing, but think about what the 30 year bond rate is. For there to be a no-arbitrage condition on the yield curve, the 30 year rate is basically an estimate what the average expected 30 day rate is going to be for all periods between now and 30 years from now, so you get the same answer.”

The practical solution to this is “There’s no perfectly defensible answer.” When you make a calculation that requires a RFR, and you expect others to read it, you simply have to say what RFR you used, and preferably where that number came from. If others want to use a different rate, they will.

If you are reading something that does a calculation that depends on the RFR, then you need to look at what they use, and see if it’s different from what you like to use instead.

What’s not cool is to switch between using short term rates and long term rates depending on what you want the answer to be. If you use short term rates to calcuate stuff, stick with that unless there is real reason to change it (which is typically about expected holding periods and/or reblance frequencies). Switching between short term rates and long term rates to figure out which gives you the best looking answer is manipulation.

Or, if you are on the buy side and want to be extra careful, you can do a scenario analysis using both short and long term rates and see how much of a difference it makes.

You do have a point that - for countries with a ZIRP policy - using short term rates to discount expected earnings 10 and 20 years into the future is disingenuous and implicitly assumes that ZIRP will never end. So perhaps discounting the first 5 years of data with graduated discount rates to reflect the termination of ZIRP makes some sense when the yield curve is highly inclined. We haven’t seen yield curves this steep for this long in recent history (if ever, in the US), so that may make some sense in the current environment if the yield curve is highly sloped one direction or another.

Finally, it’s interesting to query people and figure out what their approach to the RFR is and having the discussion about “why don’t you do it this way” or “let’s see what the differences end up being,” but (as a piece of advice) there’s just not a lot to be gained by pounding your colleague’s heads and insisting that they are doing it wrong.

The best you can do is to do the calculation yourself and compare the prices that come out and ask “do these differences change our investment process and/or results in any significant way.” Depending on how your process works, it may or may not make much of a difference. If you are doing traditional value investing, it most likely won’t, because you’ll be applying a margin of safety, which should be much larger than any differences this will produce.

If you have a quant-driven process, it’s possible that this will affect your portfolio composition in unexpected and nonlinear ways, so it might make a difference and would require substantial backtesting. Even if the portfolio composition is different, it’s still possible that the portfolio’s performance might not be, so that’s a major research project if your organization has the budget for it.

Well don’t ER reports chronically tend to be too bullish in their recommendations ?

It’s good for business.

In the end, the risk free rate that you use is probably the least made up part of the model anyway, so I doubt it matters.

However, for the sake of argument, yes, you should interpolate the term rate from a yield curve.

Additionally, you might not actually want to use a “risk free” rate, which I assume to be the base libor or swap curve, since cost of funding or other risk related spreads are different depending on the application.

The risk free rate might be more objective than other variables, but the choice of RFR does actually matter. The discount rates you use tend to exihibit some of the biggest sensitivities in the final value out of all the variables alongside the assumptions of growth.

I’m thinking a spot curve matching cash flow periods would be best in this case to discount them at their proper rates. But like mentioned before, if the curve isn’t too sloping, it generally isn’t really worth the effort, and something along the lines of a 10-year T bond should suffice (or the 10-year spot rate for a non-dividend paying company?)

However, the common practice of using the 1-year T-bill rate for all the periods, including the discount rate for terminal value will always overestimate your security. Even though on the sell-side it’s supposedly ‘good for business’, an adept investor should recognize the faulty derivation for such a calculation.