2 Numbers To Understand While Investing In Stock Markets
An introduction to understanding risk-free rates (RFR) and equity risk premiums (ERP) for India and US
Hi 👋,
Today, I thought I will do an educative post.
I am currently in the process of valuing Kotak Mahindra Bank and Nuvama Wealth, but I haven’t formally written yet.
I just finished watching the whole 27 lecture series taught for MBAs by prof. Aswath Damodaran at NYU Stern. I had done this course last year too, after doing his undergrad course. (This is the latest course link I just finished).
Some of you may ask why I did the same courses again. Well two reasons:
The commentary by Prof. Damodaran is what is engaging for me. I have already read 3 of his books, so the content is not new. It is his commentary on latest happenings which I find very engaging.
(I learnt a new phrase: “There’s a many slip between the cup and lip”😅)I love the latest examples which he covers.
Anyway, In this post (relatively short 😁), let us discuss what is US’s and India’s risk-free rate and Equity Risk Premium (ERP), how do you calculate them, and why India’s 10Y bond rate is not risk-free.
NOTE: I wanted to calculate whether NIFTY50 is Overvalued, but it skipped my mind while writing this post. Once you read this post, you may want to check out my post on NIFTY50 index valuations here. Both are related.
Let us dive in.
You can check my last post on Bajaj Finance’s fundamental valuation here.
If you are an investor, the risk-free rate and equity risk premium are the most important number to know.
I had written a high level conceptual post earlier titled - “How much would you pay for $1 forever?”. I tried explaining how one should approach an investment, w.r.t certainty and uncertainty of outcome.
In today’s post, let us dig slightly deeper and understand:
How do you understand the risk-free rate and equity risk premium?
How to calculate them?
Where are they used?
What is a risk-free rate (RFR)?
A risk-free rate is defined as the rate or return which you can expect from an asset which has the following properties (An Asset is anything which is able to make money for you: be it land, business, stock, bonds etc.) :
Your expectation of return = Your actual return
An asset you bought for $10 giving you 2% return actually delivers $12 next year.
There is be no default risk i.e. there should not be any risk for not getting your money back.
This essentially excludes any asset issued by a private player.There should not be any reinvestment risk.
What does this mean?
Well, if you buy a government bond for 5 years for $1000 with 5% coupons paid yearly. You will get $50 as interest coupons per year for next 5 years.
Now, if you wish to invest that $50 which you get next year, you should get the same 5% rate.
But as you might have guessed, all points are too ideal to be true.
Governments do defaults: on local debt and foreign debts
And, We cannot predict at what rate will that new $50 will be reinvested at in future.
However, for all practical purposes we can assume that:
Most stable governments will honour its promise.
For a 5-year/10-year valuation window (while valuing companies) , a 5-year/10-year treasury bond rate should do just fine.
The present value effect of using year-specific rates tend to me small for most cases ( Fig 1).
As shown, if you invest $1000 in the current year, you will get $50 coupons per year and $1050 in your 5th year. By changing the bond rates (top case) and keeping rates constant (bottom case), the present value of the bond changes by only $3 or 0.3%.
Hence for most practical purposes, we assume the 5y or 10y bond rate issued by a stable government to be close to risk-free (after adjusting for country’s default spread - explained in coming section)
Now, that we have understood the definition of risk-free rate, what is the risk-free rate for India and US?
How to calculate risk-free rate of India and US?
For most purposes, people do a 10 year discounted cash flow valuations (Your valuation window should be equal to the treasury bond rate tenure. Essentially, do duration matching).
The current 10Y T-bond rate for US is around 4.49% and for India, it is around 7.138%.
Now, the question is, should we consider these rates to be the risk-free rates?
Short answer: NO.
India is a Baa3 rated country, and US is Aaa rated country (as per Moody’s). You can check a country’s rating here.
Each rating class has a spread (or percentage points, which is attributable to how risky the country’s economy is).
Now, we can calculate the risk-free rates using 3 methods, each giving us different values, and this is where we need to make our judgement call.
Method 1: Checking the default spread from the ratings
All Aaa rated countries have the spread value of 0%, however, Baa3 rated countries have spread value of 2.39% (we can check the riskiness (also called spread) from this table.)
Once we get these spreads, what we need to do is to subtract these values from the original 10Y bond yields.
For US, the risk-free rate becomes 4.49% and, for India, it becomes 4.75%.
Method 2: Checking the Sovereign CDS market.
Sovereign CDS (Credit Default Swaps) market is an insurance market.
Whenever you buy any countries bond, you can buy CDS as an insurance.
These rates change daily and gives updated pictures of what is happening around the world.
However, when any major real world event happen, the rates change drastically, sometimes overreacting.
You can simply search on google US 10Y Bond CDS or India 10Y bond CDS to get the latest rates in basis points i.e. divide the value by 100 to get in % terms.
For US, it is 43.11 at the moment, i.e, 0.4311%.
For India, it is 92.60, i.e, 0.9260%.
After subtracting these rates from 10Y bond rates, we get:
US risk-free rate: 4.05%
India risk-free rate: 6.21%
To sum the results up so far, we get the following:
From the default spread calculations, we get the RFR (risk-free rate) of US close to RFR of India.
But, is it really the case?
Are we saying that India is as safe as US when it comes to investments?
I dont think this should be the case. If yes, why should the country ratings be different?!
Here, The CDS rates gives a clearer picture.
A quick way to check would the following, also you can call it as method 3.
Method 3: Extrapolate India’s Risk-Free rate from US’s rate
US’s RFR is roughly 4.27% (average of default and CDS).
We can calculate India’s RFR as:
India's RFR = (1+ US RFR) x (1 + expected inflation in India)/(1+expected inflation in US) - 1US has a bond called TIPS (Treasury Inflation Protected security). As the name suggests, it gives you a return which is inflation protected. For example, if the expected inflation is 3% and TIPS rate is 1%, you will get 4% as your yield.
Current US TIPS 10Y TIPS rate is 2.18%.
If we subtract the US TIPS 10Y rate from US T-bond 10Y rate, we will get the expected inflation in US.
expected inflation: 4.27% - 2.18% = 2.09%
What is the expected Inflation in India? Well, in India, there is nothing equivalent to TIPS which is actively traded. So, we will go with what Statista and consider the expected inflation to be 4% (check here).
Therefore, India RFR = (1 + 4.27%) x (1+4%)/(1+2.09%) -1 = 6.22%
As you can see, this value is almost equal to the value which we got from CDS spread.
Here we have calculated the RFR from different methods.
Based on our current understanding, we took a call that CDS (method 2) or Extrapolation (method 3) would be the right approach to get the risk-free rates for India, given that the RFR for India and US cannot be so close to each other.
Now, that we have RFR nailed down, we can proceed to get Equity Risk Premiums(ERP).
What is Equity Risk Premium (ERP)?
The word premium means “a value in excess of that normally or usually expected”
Equity Risk Premium means since we are investing in equities, we are taking a risk with our capital, and we understand that we will not be able to realize a value equal to our expectations (also called uncertainty in our investment).
For this uncertainty, we expect additional percentage points over the risk-free rate.
This percentage points are called Equity Risk Premiums (ERP).
How to calculate Equity Risk Premium (ERP)?
Calculation of ERP is slightly tricky.
We can look at the past data to check what the ERP has been, but it comes with too much of noise.
The oldest traded market is the US.
Fig 3 shows the arithmetic and geometric averaging results from 1928. The ERPs go from lowest of -4.11% to highest of 7.62%.
If you were to choose the ERP, what ERP would you choose?!
If we go with historical ERPs, we are assuming that the market has more or less remained the same, which is not true, and also the variation in values is too high. (These days most tech stocks are running the show in markets which was not the case before this century)
To answer this question, Prof. Damodaran suggests calculating a more forward-looking ERP called Implied ERP.
Without going too much into technicality, we can take the result from his website (Check here)
The May 2024 ERP is 4.40%, previous month it was 4.23%.
Prof. Damodaran tracks this ERP on a month on month basis.
I have tried calculating this value for Indian markets but the data is missing. I wrote an email to NSE as well to see whether they can provide the buybacks data and dividends data in market points - which is needed to calculate these implied ERPs. They replied that they don’t keep a track of buybacks in market points terms.
However, we have a solution.
We can calculate our minimum expected returns from US data and scale it to Indian Rupee terms, just the way we did for risk-free rates.
Why is this thing possible?
Well, because markets are very much correlated now. This was not the case earlier. This article explains the increasing correlations which is observed in the markets nowadays.
So, how should we calculate our minimum expectations from markets today - in US and in India.
If our investment horizon is 10 years, we can add 10Y risk-free to the current ERP.
Therefore, 4.27% + 4.40% = 8.67% would be our minimum expectations of investing in US equities - say S&P 500 - considering our 10Y time frame
Since, India is riskier than US, we will need to add Country Risk Premium (CRP) to the ERP. India’s CRP is 3.21%. Therefore, we will get in Dollar terms: 4.27% + 4.40% + 3.21% = 11.82%
In Rupee term, it would be (1+11.82%) x (1+4%)/(1+2.09%) -1 = 13.90%
(You can do the same for 5 year time frame or 1 year time frame)
This minimum expectation is also called cost of equity.
(Additinal information : Whenever ERPs increase, people expect more from the market for the risk they are taking. Whenever the ERP increases alot or is continuously increasing, the stock prises has collapsed or is in downturn. Since RFR+ERP = Cost of Equity, the discount factor i.e coe increased in your free cash flow to equity valuation, thereby decreasing present value of equity)
Where is this Cost of Equity (COE) used?
This Cost of Equity is used whenever we are trying to value a firm using Free cash flow to Equity (FCFE) or in calculation of cost of capital (also called WACC), which is then used in Free Cash Flow to Firm (FCFF) valuation.
This is a really important parameter for all investor.
If any company is having its ROE greater than its COE, it is adding value to the equity shareholders. If not, the management is destroying value for the shareholders.
I took the following picture from Prof. Damodaran’s slide.
Fig 4 shows that in India, around 34% of companies have ROE> COE. All the numbers are in dollar terms. For calculating the ROE, COE in Indian Rupee, one would need to scale it based on the process we discussed above.
As long term investor, our only job would be to find and keep a track of such companies which are able to generate positive value for us.
I hope you found this post helpful.
See you in next post.
Thank you for your time.