What number should I use for risk-free return?

[mlwl8521]

Most of us have taken enough exams to see CAPM questions where they assume the Risk-Free Rate of Return is 4% or something like that.
The textbook definition of RFR is whatever we can get “without any risk”.
In real life, does that mean “without any risk” or “without any reasonable risk”?
Check out this link:
http://www.treasury.gov/resource-ce...interest-rates/Pages/TextView.aspx?data=yield
If you were to do a CAPM demonstration or a Black Scholes demonstration, what would you put down as the Risk Free Rate of Return?
Would you do 3.46% because that’s what you get for a 30-year instrument? Or would you say 0.12% because that’s what you get for 1 year?

 

[Oscar]

In valuation practice you calculate the risk free rate based on the so called “Svensson Yield Curve”. What the SvenssonYield Curve does is to calculate based on the spot rates of treasury bonds maturing for every year of the next 30 years a risk-free rate for every year. This rates often then are converted to one risk-free rate for the whole time period of the next 30 years.
If you google a bit you’ll find plenty of information on this topic. For instance check out his link:
http://www.finexpert.info/fileadmin/user_upload/downloads/pdf/notes_Chai...

 

[MrSmart]

’Oscar’ wrote:
In valuation practice you calculate the risk free rate based on the so called “Svensson Yield Curve”. What the SvenssonYield Curve does is to calculate based on the spot rates of treasury bonds maturing for every year of the next 30 years a risk-free rate for every year. This rates often then are converted to one risk-free rate for the whole time period of the next 30 years.
If you google a bit you’ll find plenty of information on this topic. For instance check out his link:
http://www.finexpert.info/fileadmin/user_upload/downloads/pdf/notes_Chai...

Never heard of this before. Usually, the risk free rate should follow a treasury security with an appropriate maturity depending on the time period of interest. Usually 5 or 10 years for CAPM.

 

[Oscar]

This is common practice for valuation - you will find this approach also amongst valuation professionals.
The problem with your approach is that it implies a flat yield curve which in reality does not exist.
The Svensson approach for risk-free rates takes into consideration the current yield curve as per T-Bills spot rates and calculates a risk-free rate out of these.

MrSmart wrote:

’Oscar’ wrote:
In valuation practice you calculate the risk free rate based on the so called “Svensson Yield Curve”. What the SvenssonYield Curve does is to calculate based on the spot rates of treasury bonds maturing for every year of the next 30 years a risk-free rate for every year. This rates often then are converted to one risk-free rate for the whole time period of the next 30 years.
If you google a bit you’ll find plenty of information on this topic. For instance check out his link:
http://www.finexpert.info/fileadmin/user_upload/downloads/pdf/notes_Chai...

Never heard of this before. Usually, the risk free rate should follow a treasury security with an appropriate maturity depending on the time period of interest. Usually 5 or 10 years for CAPM.

 

[onlysimon]

‘real life’ means you’ll get sold a 60/40 portfolio. the bonds will be on average AA rated corporates with 5yr duration.
today that is 2.08% yield.

 

[bchad]

It’s technically supposed to be a zero-coupon treasury security with maturity set to the your length of your investment horizon. So for stocks, one often uses the 10y treasury spot rate (sometimes the yield if you are too lazy to bootstrap). For options and futures, you often use the 90d t-bill rate or possibly the 30d rate because the derivitves have maturity/expiry dates that are close on the calendar.
I tend to use the 90day tbill rate because we rebalance every month. I could use the 30day I guess but the 90d are more common and thus reflect more realistic cash scenarios in my mind.
A lot of people use whatever makes their numbers look best. Whichever one you use, just make sure you have an argument for using it and understand what the arguments are for other rates if you get asked about it.

 

[MrSmart]

’Oscar’ wrote:
This is common practice for valuation - you will find this approach also amongst valuation professionals.
The problem with your approach is that it implies a flat yield curve which in reality does not exist.
The Svensson approach for risk-free rates takes into consideration the current yield curve as per T-Bills spot rates and calculates a risk-free rate out of these.

MrSmart wrote:

’Oscar’ wrote:
In valuation practice you calculate the risk free rate based on the so called “Svensson Yield Curve”. What the SvenssonYield Curve does is to calculate based on the spot rates of treasury bonds maturing for every year of the next 30 years a risk-free rate for every year. This rates often then are converted to one risk-free rate for the whole time period of the next 30 years.
If you google a bit you’ll find plenty of information on this topic. For instance check out his link:
http://www.finexpert.info/fileadmin/user_upload/downloads/pdf/notes_Chai...

Never heard of this before. Usually, the risk free rate should follow a treasury security with an appropriate maturity depending on the time period of interest. Usually 5 or 10 years for CAPM.

Why does it imply a flat yield curve? It doesn’t.
Your risk free rate of choice should be the opportunity cost of investing in a risk free security of the same time period as the investment of interest. Usually the 10-year T-Bond rate for calculating the cost of a equity on a stock. And shorter RFR maturities for short term stock trading and thus lower COE, natually.
Same goes for Black-Scholes modeling. But I’m not too familliar with BS option pricing. I might look it up for you if you’d like, I’m assuming it’s less than 10 years in most cases though.

 

[Oscar]

MrSmart wrote:

’Oscar’ wrote:
This is common practice for valuation - you will find this approach also amongst valuation professionals.
The problem with your approach is that it implies a flat yield curve which in reality does not exist.
The Svensson approach for risk-free rates takes into consideration the current yield curve as per T-Bills spot rates and calculates a risk-free rate out of these.

MrSmart wrote:

’Oscar’ wrote:
In valuation practice you calculate the risk free rate based on the so called “Svensson Yield Curve”. What the SvenssonYield Curve does is to calculate based on the spot rates of treasury bonds maturing for every year of the next 30 years a risk-free rate for every year. This rates often then are converted to one risk-free rate for the whole time period of the next 30 years.
If you google a bit you’ll find plenty of information on this topic. For instance check out his link:
http://www.finexpert.info/fileadmin/user_upload/downloads/pdf/notes_Chai...

Never heard of this before. Usually, the risk free rate should follow a treasury security with an appropriate maturity depending on the time period of interest. Usually 5 or 10 years for CAPM.

Why does it imply a flat yield curve? It doesn’t.
Your risk free rate of choice should be the opportunity cost of investing in a risk free security of the same time period as the investment of interest. Usually the 10-year T-Bond rate for calculating the cost of a equity on a stock. And shorter RFR maturities for short term stock trading and thus lower COE, natually.
Same goes for Black-Scholes modeling. But I’m not too familliar with BS option pricing. I might look it up for you if you’d like, I’m assuming it’s less than 10 years in most cases though.

What you said is correct. However you have a reinvestment assumption on the earnings of your risk-free rate (also in CAPM). And in order to model this reinvestment assumption you need a yield curve as per existing spot rates. I’m aware that people often use just a time-equivalent T-Bill rate as risk-free rate, however this is not (theoretically) 100% correct and always a simplification.

 

[mlwl8521]

It is fascinating how (what appears to be) a simple question can draw different points of views from experienced and credentialed finance professionals. Thank you all.

 

[MrSmart]

’Oscar’ wrote:

MrSmart wrote:

’Oscar’ wrote:
This is common practice for valuation - you will find this approach also amongst valuation professionals.
The problem with your approach is that it implies a flat yield curve which in reality does not exist.
The Svensson approach for risk-free rates takes into consideration the current yield curve as per T-Bills spot rates and calculates a risk-free rate out of these.

MrSmart wrote:

’Oscar’ wrote:
In valuation practice you calculate the risk free rate based on the so called “Svensson Yield Curve”. What the SvenssonYield Curve does is to calculate based on the spot rates of treasury bonds maturing for every year of the next 30 years a risk-free rate for every year. This rates often then are converted to one risk-free rate for the whole time period of the next 30 years.
If you google a bit you’ll find plenty of information on this topic. For instance check out his link:
http://www.finexpert.info/fileadmin/user_upload/downloads/pdf/notes_Chai...

Never heard of this before. Usually, the risk free rate should follow a treasury security with an appropriate maturity depending on the time period of interest. Usually 5 or 10 years for CAPM.

Why does it imply a flat yield curve? It doesn’t.
Your risk free rate of choice should be the opportunity cost of investing in a risk free security of the same time period as the investment of interest. Usually the 10-year T-Bond rate for calculating the cost of a equity on a stock. And shorter RFR maturities for short term stock trading and thus lower COE, natually.
Same goes for Black-Scholes modeling. But I’m not too familliar with BS option pricing. I might look it up for you if you’d like, I’m assuming it’s less than 10 years in most cases though.

What you said is correct. However you have a reinvestment assumption on the earnings of your risk-free rate (also in CAPM). And in order to model this reinvestment assumption you need a yield curve as per existing spot rates. I’m aware that people often use just a time-equivalent T-Bill rate as risk-free rate, however this is not (theoretically) 100% correct and always a simplification.

The risk free rate is a variable used in the context of Kd and Ke, so the YTM is not really relevent, hence why reinvestment is not taken into account, as far as I remember from reading valuation textbooks. Someone correct me if I’m wrong with a legitmate source.
The T-Bill RFR is not commonly used actually, most of the rates are long term T-Bonds, as I’ve mentioned earlier.

 

[Oscar]

Dear Mr. Smart,
I advise you to read the following link from the “godfather” of valuation Damodaran:
http://people.stern.nyu.edu/adamodar/pdfiles/papers/riskfreerate.pdf
There he describes (1) why the reinvestment assumption in estimating the risk-free rate matters and (2) why the yield curve is indeed important in estimating the risk-free rate, especially in markets with inverted or high upward sloping yield curves.
As I told you, I am well aware that a lot of practitioners follow the approach described by you.
However, a lot also do it according to the way described above. As a matter of fact f the International Association of Valuators (IACVA) and the German Valuation Standard (IDW) recommend the approach described by me.
Best, Oscar

 

[Oscar]

double

 

[MrSmart]

’Oscar’ wrote:
Dear Mr. Smart,
I advise you to read the following link from the “godfather” of valuation Damodaran:
http://people.stern.nyu.edu/adamodar/pdfiles/papers/riskfreerate.pdf
There he describes (1) why the reinvestment assumption in estimating the risk-free rate matters and (2) why the yield curve is indeed important in estimating the risk-free rate, especially in markets with inverted or high upward sloping yield curves.
As I told you, I am well aware that a lot of practitioners follow the approach described by you.
However, a lot also do it according to the way described above. As a matter of fact f the International Association of Valuators (IACVA) and the German Valuation Standard (IDW) recommend the approach described by me.
Best, Oscar

I was about to get into Investment Valuation by Damodaran this week actually, it’s sitting on my desk at the moment.
Most of the other valuation textbooks I’ve read differ from Damodaran’s assumptions (If we are both not mistaken), including the CFAI textbooks I believe.

Quoted from the link you gave: “Given that the difference between the 10-year and 30-year bond rates is small, and that it is much easier estimating equity risk premiums and default spreads against the former rather than the latter, we believe that using the 10-year bond rate as the riskfree rate on all cash flows is a good practice in valuation, at least in mature markets. In exceptional circumstances, where year-specific rates vary widely across time, we should consider using riskfree rates that vary across time.”

I still fail to see why reinvestment is important for choosing the RFR. Reinvestment assumptions can vary widely between companies and financing methods. Therefore the opportunity cost for reinvestment should be either held constant at the yield (IRR and YTM definition), or ignored altogether to keep it consistent.

In any case, reinvestment make up a very small part of actual YTM, and the fluctating short term rates should not put a significant dent on the number, except in unqiue markets and situations.

 

[Oscar]

MrSmart wrote:
Most of the other valuation textbooks I’ve read differ from Damodaran’s assumptions (If we are both not mistaken), including the CFAI textbooks I believe.

It is a basic assumption in DCF that there has to be time equivalence between the annual cash-flows and the risk-adjusted discount rate (WACC). Having this said, it is theoretically not correct to discount a cash-flow in Year 1 with the same risk-free rate as a cash flow in year 30. By using a yield curve you basically use the correct time equivalent risk-free rates for the annual cash-flows. This is what Damodaran is pointing out - and the assumption on time equivalence is something you’ll find in most of the valuation and finance literature.

MrSmart wrote:
Quoted from the link you gave: “Given that the difference between the 10-year and 30-year bond rates is small, and that it is much easier estimating equity risk premiums and default spreads against the former rather than the latter, we believe that using the 10-year bond rate as the riskfree rate on all cash flows is a good practice in valuation, at least in mature markets. In exceptional circumstances, where year-specific rates vary widely across time, we should consider using riskfree rates that vary across time.”

As said above, Damodaran suggests that under certain circumstances a practical apporach as per his quote might be feasible. Hoewever, he also points out when such an approach would lead to misleading results:
” When would it make sense to use year-specific riskfree rates? If the yield curve is downward sloping (short term rates are much higher than long term rates) or excessively upward sloping, with long term rates exceeding short term rates by more than 4%, there is a payoff to being year-specific. In market crises, for instance, it is not uncommon to see big differences (in either direction) between short term and long-term rates.”
Remember: In the years following the financial crisis we had in fact a high upward sloping yield curve.

MrSmart wrote:
I still fail to see why reinvestment is important for choosing the RFR. Reinvestment assumptions can vary widely between companies and financing methods. Therefore the opportunity cost for reinvestment should be either held constant at the yield (IRR and YTM definition), or ignored altogether to keep it consistent.
In any case, reinvestment make up a very small part of actual YTM, and the fluctating short term rates should not put a significant dent on the number, except in unqiue markets and situations.

This has basically also to do with the time-equivalence assumtion and an non-flat yield curve. Your assumpption is only a correct approximation if the yield curve is flat or has only a small slope. Damodaran describes the reinvestment assumption as of page 6 of his article.
As a summary, using a fix rate is always a (practical) compromise. The important thing is to be aware when this compromise works and when not. And for this you must have a look at the yield curve.
Best, Oscar

 

[bchad]

In equities, the uncertainty in the cash flows is typically so noisy that small year-by-year corrections in the discount rate are just not enough to move the needle much, and this is one reason why they tend to be ignored. There is uncertainty in the cash flow projections, and here is uncertainty in the equity risk premium that should be applied that is typically orders of magnitude greater than the corrections you are likely to use on the RFR based on the yield curve. However, if you are doing a DCF on something with steady predictable cash flow, like a utility, and the yield curve is highly sloped, you may get some kind of payback in terms of an improved valuation that promotes a better decision.
In fixed income, these kids of corrections are more relevant (e.g. Z-spread or OAS calculations), but that’s because the cash flows here are generally more predictable (especially if hey are not floating rates) and because the risk premiums are much smaller than in equities.

 

[Oscar]

bchad wrote:
In equities, the uncertainty in the cash flows is typically so noisy that small year-by-year corrections in the discount rate are just not enough to move the needle much, and this is one reason why they tend to be ignored. There is uncertainty in the cash flow projections, and here is uncertainty in the equity risk premium that should be applied that is typically orders of magnitude greater than the corrections you are likely to use on the RFR based on the yield curve. However, if you are doing a DCF on something with steady predictable cash flow, like a utility, and the yield curve is highly sloped, you may get some kind of payback in terms of an improved valuation that promotes a better decision.
In fixed income, these kids of corrections are more relevant (e.g. Z-spread or OAS calculations), but that’s because the cash flows here are generally more predictable (especially if hey are not floating rates) and because the risk premiums are much smaller than in equities.

Agree with everything you said!
The important thing is to be aware of the underlying assumptions in order to make a proper decision on when a simplified approach (though not 100% theoretical correct) is enough and when a more sophisticated approach is needed.
Regards, Oscar