Class 4 Valuation: Risk & Risk-free rates
Class 4 Valuation: Risk & Risk-free rates
Role of the Fed, inflation & what is really risk-free
Class opening test:
You have a choice of valuing a Brazilian company, either in US$ or in R$.
Risk-free rate, Rfr for US is 2.5% & Brazil is 7.5%.
Which currency will give you a higher valuation?
a) US$, because of lower Rfr which will give a lower discount rate
b) R$, because exchange rate will be in my favour
c) Neither, both should give the same value.
If you choose a), then why not choose a currency with even lower Rfr? Go value all companies in Japanese Yen!
Currency won’t affect valuation because you are doing it in nominal term, i.e. inflation is reflected in both the rates & cashflow. The strength & weakness of a currency pair reflects the underlying inflation situation. If inflation is high in a country, the currency of that country will be lower due to lower buying power.
Whether it is in nominal terms or real terms, inflation is like an elephant in the room. If it moves, you will know. Even if you remove inflation effect by using real rates, it will affect your cashflow (weaker margins) eventually.
What about The Fed that sets rates low for past decade? What if Fed doesn’t exist? We’ll be visiting this later in the class, is not about the Fed.
Negative interest rates, how would this affect valuation? Normalise the rate by changing minus sign to positive sign? Quick fix! (Prof.’s usual sarcasm)
What risk matters to a marginal investor?
Not all risks count. Risk on a company to you, is seen through your lens only from a portfolio perspective. If you are diversified, then a lot of company’s specific risks (unsystematic risk) are diversified away. Your only risk is the market risk (systematic risk that can’t be diversified away).
The only risk you should be concern of, is risk that you cannot diversify away.
What if you are a highly concentrated investor, to the extent of owing the business? Then you have control premium? Remember $20 envelope?
The benefit of diversification though will only get smaller as your portfolio adds in more stocks. The risk that you can’t diversify away is called the beta, β in Capital Asset Pricing Model (“CAPM”).
In a market portfolio, β=1 & there’s no transaction costs. The beta captures all the systematic risks, whether it’s interest rate risks, economic risks or inflation risks; risks that you can’t diversify away.
To distinguish these different risks, Arbitrage Pricing Model & Multi-factor Model are thus developed to assigned different value to these individual betas.
Conclusion: A stock that earns higher returns, means it has higher risk against the market. Hence, we fall back to the market portfolio to give the best risk adjusted return. The only way to earn more then, is through leverage of an index fund.
Risk-free rate is the first building foundation in valuation because if you don’t know how much a guaranteed return you can make, then you can’t build things up to value a risky asset.
Next, is the market risk premium.
Lastly, a β to measure the company’s specific risk against the market.
Cost of Equity = Rfr + β * (market risk premium)
Rfr is the easiest to measure, but not that easy actually. To be risk-free, there must be:
no default risk, not a single iota
no re-investment risk (to forecast a 10-year cash flow, you can’t use a 5-year t-bill with the assumption that it will be renewed for another 5 years at the same rate)
Thus, the following matters to get the correct Rfr:
time-horizon of cashflow
currency involved
not all govt bonds are risk-free even if is on own currency (where they can print money which would lead to currency debasement. Defaulting & borrow again at higher rate is better than debasing & not being able to borrow the same quantum.)
Class test 1 - matching the duration
In valuing a US cash flow that is very long term, which of the following is the correct Rfr to use:
a. 3-mth T-bill (4.42%) = > definitely not
b. 10-yr T-bond (3.88%) =>mostly used Rfr in order to find a comparable corporate bond in measuring default spread
c. 30-yr T-bond (3.97%) => is hard to find 30-yr corporate bonds even as you try to match the duration
d. TIPs, inflation-indexd (1.53%) =>only if your cashflow is also in real-terms with inflation removed
(You can actually match individual cash flow on the t-bill rate on a 30 yr yield curve as a valuation purist but it will make NPV tedious)
Can the US default? Keep this at the back of your mind because in 2011 S&P rating agency actually downgraded US from AAA to AA, with a negative outlook for the first time.
Class test 2 - a test on default risk in a common regional currency
If you are valuing a company in the EU, which of the above 10-yr Euro bonds will you use as risk-free rate? (All the bonds above are in Euro currency.)
Keyword here is default risk. Remember that if there’s an iota chance of default, then it is not risk-free. Hence, the only country’s Rfr you can use is Germany’s 2.25% (AAA rated), regardless if the company is in France or Italy.
You’ll have plenty of chance to punish the high risk company in Greece, but not via Rfr.
Class test 3 - second test on default risk for emerging market
India has a 10-year Rupee bond that is yielding at 7.34% but it also has a default risk. This default risk is actually already implied in the rate published. Hence, you’ll need to adjust downward (not upward to double count!) via a default spread to get an actual Rfr.
The default spread can be obtained via following 3 options:
A US$ or EU bond issued by the emerging country minus by the emerging country’s “pre-adjusted Rfr”
CDS spread for the emerging country, can be taken directly though there’s friction cost (counterparty risk) which needs to be taken out
If the above can’t be obtained, using the average spread for similar emerging countries with the same country rating
Hint: The 10-yr gilt of UK is not Rfr, so is the 10-yr gov bond of Japan. They need to be adjust upward using the spreads approach above.
Class test 4 - real Rfr means there’s no currency
First, use real Rfr only in very high inflationary environment. Otherwise, stick to nominal rates because everything else is in nominal, you pay & receive things in nominal terms.
Thus, this is where TIPS rate can be used when in real rates, even if in a country like Ghana. However, it is better to switch the currency in an adjacent country’s currency with that country’s nominal Rfr (South Africa, maybe).
Why do Rfr varies in different countries (see chart below)?
It varies because of the country’s inflation. Hence, this is why currency doesn’t matter, Rfr is the mechanism to equalise.
In conclusion, even if the company’s cashflow doesn’t change, nothing about the company’s change, a change in inflation will change the Rfr which would trigger a change in valuation.
Best practice is to make the Rfr in a seperate input change because it is not constant when you do valuation modeling.
Another sanity check or method to get Rfr of any country is to know the country’s inflation rate, & US’s inflation & Rfr.
Say if US’s Rfr is 2%, with inflation of 4%; and Country X has inflation of 10%, here’s the formula & result.
Rfr of Country X = (1+2%)*(1+10%)/(1+4%) -1= 7.8%
1 last test - what happens if the T-bond rate is too low?
In Jan 2022, the 10 year t-bond was 1.51%, this was low by historical standard. Assuming you are valuing a US company, would you adjust it to a normalise rate of say 4-5%?
You can’t.
The purpose of Rfr is to give an opportunity cost or an alternative to a risk-adjusted asset that you valued. If you think the risk asset is overvalued, you would of course choose to invest in the risk-free asset, right? Now where do you find this risk-free asset with an adjusted Rfr of 4-5%? It is not available!
Finale note on risk-free rate
T-bond rate started to fall in 1980, all the way to 2020/21. Over the same period inflation rate has gradually fell as well together with the real GDP growth.
It is important to note that the Fed Fund Rate is an overnight borrowing rate for banks. The Fed only influence the borrowing costs between the banks.
This is very similar to the story of a rooster that crows every morning. All animals in the farm thinks that the rising of the sun in the morning was due to the crowing of the rooster, which in fact it was the other way around.
The Fed is reacting to inflation rate, which can be explained by the Fisher equiation of Nominal rate = real rate + inflation rate. If inflation rises, nominal rates need to rise.
When you look back at the past decade, both inflation & real GDP growth are low, & hence the low T-bond rate! The Fed effect was maybe like only 0.25%. The perception strength of the central bank is what “influencing” the rates. Otherwise, what central bank does has absolutely no effect on risk-free rates, like what Japan is experiencing.
Hence, to know what are the expected Rfr for this year. There are only one answers to guess. Not what the Fed will do, but what the inflation will be at.
Lastly, about Negative Rfr.
In 2022, Swiss, Jap & Euro are 3 countries/currencies that are still having negative interest rate. Does that mean valuation in these currencies will be sky high?
No. We’re forgetting about cash flows. In these economies, they are in negative Rfr to stimulate growth, meaning fundamentally companies in these countries are also in weak. Hence, free cash flows are also in negative growth!
Next, we’ll talk about Equity Risk Premium.
// end of Class 4 Valuation