Hi,
a rise in the risk free rate leads to a decline in the cost of equity when beta is >1 and vice versa. I get it analytically from the CAPM but how would one explain this without the formula?
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A rise in the risk free rate leads to an increase in cost of equity always. where did you get this info
This is not accurate. You're not considering changes to MRP.
No, I am considering changes to MRP. If Rf increases, Rm will not stay constant.
read the post off wrong, buried myself in shame
If you got that wrong you probably got a lot of other questions wrong too... so probably.
We all make mistakes
An increase in the risk free rate is always going to increase cost of equity. Beta doesn't even affect the relationship between the risk-free rate and cost of equity - it's only a coefficient to the market risk premium.
Think about it this way - if the risk free rate is 2% and the cost of equity for a certain company is 10%, the market is essentially thinking that based on this company's risk profile and how the market is performing at large, its equity demands an 8% premium to be compensated for that risk. If you up the risk free rate to 3%, the company's cost of equity isn't going to still be 10% - since the risk profile justifies an 8% premium, the cost of equity will now be 11%. Note that the increase in the risk-free rate did not affect the beta of the company at all, so the risk profile remains the same. This is basically how you'd reason about how CAPM works.
Incorrect. Consider changes to market risk premium.
Mathematically op is actually correct.
How do you figure? All beta does is either magnify (if >1) or dampen (if 1) the effect of market risk premium...Rf and Rm have a purely covariant relationship. All else equal, an increase in Rf leads to an increase in the cost of equity because the market is just assigning the exact same risk premium but atop the additional increase in the risk-free rate. He's conceptually and mathematically incorrect.
So I haven't really thought super deep into this but here's my train of thought (I approached this from a "how is OP correct" perspective so most of the work I did was from the perspective of trying to confirm OP's statements, which may well have impacted my train of thought).
CoE = Rf + B x (Rm - Rf) where let's assume (Rf = 3% and Rm = 10%) since we are testing CoE sensitivity to changes in Beta and Rf let's look at following cases:
Op Said "rise in the risk free rate leads to a decline in the cost of equity when beta is >1"
When B = 2 we have CoE = 3 + 2*(10-3) = 17
If we keep B static and increase Rf to 5% we then get: CoE = 5 + 2*(10-5) = 15
My thought process was that you are correct, B just dampens or magnifies MRP but MRP is a function of Rm and Rf (if we assume to use long run Rm (20, 30, 40 year averages) to mitigate some of the shortfalls of CAPM, then a short term change in Rf isn't likely to also impact Rm, thus it stays static at Long-Run average of 10ish%.
So essentially B is dampening or magnifying BOTH Rm and Rf. If we ONLY focus on Rf in the equation for a moment we get the following formula: CoE = Rf - BRf
Thus if B is > 1 we are decreasing MRP by a magnified Rf where CoE = Rf - 2Rf (net decrease regardless of what Rf increases to). If B = 1 then it simplifies to Rf - Rf, if B 1 it simplifies to Rf - 1Rf thus increasing CoE.
Beta magnifies the MRP
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