Last week, the 10-year US treasury bond rate dropped to 1.75%. While it has risen since to about 2%, there can be no denying a basic fact. Government bond rates have dropped in almost all of the developed market currencies: the Euro, the British Pound, the Swiss Franc and the Yen. Since government bond rates are used as risk free rates to estimate discount rates in valuation or hurdle rates in corporate finance, there has been a great deal of hand wringing and angst among valuation practitioners on the consequences. In fact, if you allow for the increase in sovereign risk across the globe, you could argue that the "true" risk free rates are even lower than the already low government bond rates. In my previous post on the sovereign rating downgrade for the US, I noted that the default spread would have to be netted out against the government bond rate to get to the risk free rate. If, for instance, you accepted the S&P rating of AA+ for the US and estimated a default spread of 0.20% for that rating, the US dollar risk free rate right now would be about 1.80% (2% minus 0.20%).

So what effect do lower risk free rates have on value? The answer, if you follow conventional valuation practice, seems obvious. Lower risk free rates, holding all else constant, result in lower discount rates, and lower discount rates, all else held the same, will result in higher value. In fact, this seems to be the implicit message in the Fed's Operation Twist 2: that lower risk free rates are good for the economy and markets. It is also this facile conclusion that makes some practitioners uncomfortable with using today's rates in valuations; the angst gets deeper when the practitioner in question wants a "low" value for an asset (for tax assessments or to tilt the scales in a legal tussle). It is not surprising then that these practitioners flirt with an alternative: why not use "normalized" risk free rates instead of today's "abnormally" low risk free rates? The normalized risk free rates are generally computed by looking at the past: thus, the average 10-year treasury bond rate over the last 30 years, which is closer to 4%, is suggested as an option. Alluring though this option seems, not only is it the wrong solution to the perceived problem (of low risk free rates and out of control valuations), there may be no problem to solve in the first place. And here is why..

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Risk free rate = Expected inflation + Expected real growth

Viewed through these lens, it is quite clear that a very low risk free rate is not generally compatible with a vibrant high growth economy. In fact, the biggest factor driving down ten-year bond rates this year from 3.29% to 2% has been the increasing pessimism about global economic health, pushing down both expected real growth and expected inflation. That is the basis for my argument that the Fed has become a side player in this game and that its push for lower risk free rates is actually at odds with its desire that the US return to healthy economic growth.

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Note that while the overall expected return on stocks (backed out from level of the S&P 500 index and expected cash flows from stocks) has been in a fairly tight range (8%-9%), the proportions coming from the risk free rate and equity risk premium have changed. And there are consequences for value as well. To see why assume that you are valuing a mature, average risk company (growing at the same rate as the economy) with $ 100 million in cash flows to equity currently in a market where the risk free rate is 4% and the equity risk premium is also 4% (thus creating a cost of equity of 8%). Since the risk free rate is the proxy for nominal growth in the economy, this company's value is:

Value of company = 100 (1.04) / (.08-.04) = $2,600 million

Now consider valuing the same company when the risk free rate is 2% and the equity risk premium is 6%. Since the nominal growth rate expectation is down to 2%, the value of the company is:

Value of company = 100 (1.02)/ (.08 - .02) = $1,700 million

The effect on value will be greater for higher risk companies, where the risk premium is magnified, and lower for lower risk companies, but it will be significant across the board. Note that the first scenario resembles the market numbers in 2007 whereas the second is close to where we are today. The shift in risk free rates/ risk premiums may explain why stocks look cheap today, relative to historic metrics.

So, what do we do about low risk free rates? As I see it, you can choose one of four routes, ranging from dysfunctional to dynamic:

Value of company = 100 (1.04)/ (.06-.04) = $5,200 million

You will find everything you look at to be dramatically under valued, but the model is internally inconsistent. In effect, though, you are combining a crisis risk free rate with a good times risk premium/growth rate to estimate too high a value.

Value of company = 100 (1.02) / (.10 - .02) = $1,275 million

Here, the inconsistency is that you have combined a good times risk free rate with a crisis risk premium/growth rate to estimate too low a value.

I would steer away from the internally inconsistent valuations, either dysfunctional (giving you too high a number) or depressed (giving you too low a number) because your inputs are at war with each other. As for denial and dynamic valuations, I prefer dynamic valuations because I am not sanguine that reversion back to historic norms will happen soon. I can see why long term, value investors may be attracted to denial valuations but they better have a road map to their alternate pre-crisis universe, or the valuations will not come to fruition. But the bottom line about risk free rates is worth repeating. Lower risk free rates do not always translate into higher values for risky assets and it is not necessarily a "problem" that needs to be solved.

So what effect do lower risk free rates have on value? The answer, if you follow conventional valuation practice, seems obvious. Lower risk free rates, holding all else constant, result in lower discount rates, and lower discount rates, all else held the same, will result in higher value. In fact, this seems to be the implicit message in the Fed's Operation Twist 2: that lower risk free rates are good for the economy and markets. It is also this facile conclusion that makes some practitioners uncomfortable with using today's rates in valuations; the angst gets deeper when the practitioner in question wants a "low" value for an asset (for tax assessments or to tilt the scales in a legal tussle). It is not surprising then that these practitioners flirt with an alternative: why not use "normalized" risk free rates instead of today's "abnormally" low risk free rates? The normalized risk free rates are generally computed by looking at the past: thus, the average 10-year treasury bond rate over the last 30 years, which is closer to 4%, is suggested as an option. Alluring though this option seems, not only is it the wrong solution to the perceived problem (of low risk free rates and out of control valuations), there may be no problem to solve in the first place. And here is why..

1.

__The risk free rate is not just a number in a discount rate computation but an opportunity cost.__One way to think about the risk free rate is that it is the rate you will earn if you choose not to take the risky investments that are out there (stocks, corporate bonds, real estate, a business venture). So, let's carry this to its logical extreme. Let's assume that you do replace today's risk free rate (2% or lower) with your normalized rate (4%) and that the resulting high discount rate gives you a low value for your risky asset. Let's then assume that you choose not to invest in that risky asset. Where do you plan to invest that money instead? In your normalized bond earning 4%? Since it exists only on your spreadsheet, I am afraid that you will have to settle for that "abnormally" low 2% interest rate.2.

__The risk free rate is a reflection of what people expect in the overall economy for the foreseeable future.__Harking back to an equation that I have used before, note that the risk free rate is the sum of two market expectations: an expectation of inflation for the future and an expectation of real growth.Risk free rate = Expected inflation + Expected real growth

Viewed through these lens, it is quite clear that a very low risk free rate is not generally compatible with a vibrant high growth economy. In fact, the biggest factor driving down ten-year bond rates this year from 3.29% to 2% has been the increasing pessimism about global economic health, pushing down both expected real growth and expected inflation. That is the basis for my argument that the Fed has become a side player in this game and that its push for lower risk free rates is actually at odds with its desire that the US return to healthy economic growth.

3.

__The risk free asset is also where investors flee when the fear factor rises, the much vaunted "flight to safety" during crises.__But this flight does not just affect the risk free rate.... It affects risk premiums for all risky asset classes: equity risk premiums rise, default spreads on corporate bonds widen and cap rates on real estate become higher. If you define the expected return from stocks as the sum of the risk free rate and the equity risk premium, the last decade has seen changes in that composition:Note that while the overall expected return on stocks (backed out from level of the S&P 500 index and expected cash flows from stocks) has been in a fairly tight range (8%-9%), the proportions coming from the risk free rate and equity risk premium have changed. And there are consequences for value as well. To see why assume that you are valuing a mature, average risk company (growing at the same rate as the economy) with $ 100 million in cash flows to equity currently in a market where the risk free rate is 4% and the equity risk premium is also 4% (thus creating a cost of equity of 8%). Since the risk free rate is the proxy for nominal growth in the economy, this company's value is:

Value of company = 100 (1.04) / (.08-.04) = $2,600 million

Now consider valuing the same company when the risk free rate is 2% and the equity risk premium is 6%. Since the nominal growth rate expectation is down to 2%, the value of the company is:

Value of company = 100 (1.02)/ (.08 - .02) = $1,700 million

The effect on value will be greater for higher risk companies, where the risk premium is magnified, and lower for lower risk companies, but it will be significant across the board. Note that the first scenario resembles the market numbers in 2007 whereas the second is close to where we are today. The shift in risk free rates/ risk premiums may explain why stocks look cheap today, relative to historic metrics.

So, what do we do about low risk free rates? As I see it, you can choose one of four routes, ranging from dysfunctional to dynamic:

__1. The dysfunctional valuation:__You leave risk free rates at today's low levels, while your risk premiums and growth rates come from happier, more stable times. Implicitly, this is exactly what you will do, if you use equity risk premiums from historical data (Ibbotson, for instance) and earnings growth rates that reflect the "good old days". Using the example above, you would value the average risk, mature company, using a 2% risk free rate, a 4% nominal growth rate and a 4% equity risk premium:Value of company = 100 (1.04)/ (.06-.04) = $5,200 million

You will find everything you look at to be dramatically under valued, but the model is internally inconsistent. In effect, though, you are combining a crisis risk free rate with a good times risk premium/growth rate to estimate too high a value.

__2. The depressed valuation__: You could replace the risk free rate today with a higher, normalized risk free rate, while using the higher risk premiums and growth rates that characterize crisis marks. Thus, in the valuation example, you would be using a 4% risk free rate in conjunction with a 2% nominal growth rate and a 6% equity risk premium, leading unsurprisingly to a low value:Value of company = 100 (1.02) / (.10 - .02) = $1,275 million

Here, the inconsistency is that you have combined a good times risk free rate with a crisis risk premium/growth rate to estimate too low a value.

__3. The denial valuation__:You could be a normalizer, replacing current numbers with normal numbers, not just on the risk free rate but on the other inputs (equity risk premiums, cash flows, growth rates) as well. This faith in mean reversion leaves the intrinsic value of the hypothetical company stuck at $2,600 million, as risk free rates and risk premiums change, and views the crisis as "nightmare" that will soon be forgotten. Unlike the first two choices, this one is internally consistent and may, in fact, be the valuation that is used by a classic contrarian investor, who believes that markets over react and adjust back to norms over time.__4. The dynamic valuation__: You could use today's combination of a low risk free rate, high risk premium and low nominal growth to estimate a value of $1,700 million for the company. The valuation is internally consistent but the downside is that it will be volatile and change as the macro environment changes, creating discomfort for those who believe that intrinsic value is a stable number that stays unchanged over time.I would steer away from the internally inconsistent valuations, either dysfunctional (giving you too high a number) or depressed (giving you too low a number) because your inputs are at war with each other. As for denial and dynamic valuations, I prefer dynamic valuations because I am not sanguine that reversion back to historic norms will happen soon. I can see why long term, value investors may be attracted to denial valuations but they better have a road map to their alternate pre-crisis universe, or the valuations will not come to fruition. But the bottom line about risk free rates is worth repeating. Lower risk free rates do not always translate into higher values for risky assets and it is not necessarily a "problem" that needs to be solved.