How does a lower risk free rate = lower expected returns for risky assets?

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kpollar1

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Trying to wrap my head around this. I am looking at the APT model in Portfolio Management. This also relates to the the CAPM theory. According to these theories: If the risk free rate of return is lower, the expected return for an asset would be lower. If the risk free rate is higher, the expected return on an asset is higher. When I think of the risk free rate today and the fed funds rate today, it makes me think of how it translates into todays historical low rates/borrowing costs(low rates mainly due to our recent QE programs and low fed funds rate). Also, I understand that low rates mean that investors are willing to accept a lower yield (payment) for a given amount of risk. Also, I understand that investors appiitite for risk free bonds affects the yields. If more investors are buying risk free bonds, this will drive up the price of the bonds and drive down the yields. I guess what Im trying to say is: If the 10yr tbill yield is currently at 2.08%, shouldnt that be stimulating to companies and drive higher stock returns? Or, does a low risk free rate just mean that more people are buying risk free bonds and not risky assets, therfore driving down the vaules of risky assets? I guess the APT and CAPM models are just theories and not perfect but trying to grasp the big picture here. Any insight/thoughts would be appreciated. Thanks
 
kpollar1 wrote:Trying to wrap my head around this. I am looking at the APT model in Portfolio Management. This also relates to the the CAPM theory. According to these theories: If the risk free rate of return is lower, the expected return for an asset would be lower.
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Doesn’t that depend on the asset’s beta?
Suppose that:
  • rf = 2%
  • E(Rmkt) = 8%
  • β1 = 0.9
  • β2 = 1.0
  • β3 = 1.1
Then,
  • E(R1) = 2% + 0.9(8% – 2%) = 7.4%
  • E(R2) = 2% + 1.0(8% – 2%) = 8.0%
  • E(R3) = 2% + 1.1(8% – 2%) = 8.6%
If, rf drops to 1%, then:
  • E(R1) = 1% + 0.9(8% – 1%) = 7.3%
  • E(R2) = 1% + 1.0(8% – 1%) = 8.0%
  • E(R3) = 1% + 1.1(8% – 1%) = 8.7%
So whether the asset’s return increases, decreases, or remains unchanged depends on its beta.
 
Thanks for that explination, very simple and makes sense. I think I am trying to over think it.
 
I think its even more basic than all of that - simply stated the risk free rate is the starting point for valuing all assets - upon which the appropriate risk premium for any risky asset is added. The above formula points out the interesting fact that the required return may go up or down with a directional change depending on the Beta when the risk free change is reflected in stock valuation. The Beta multipliier manifests in an interesting and almost nonintuitive way. With respect to other valuation of other asset classes (like risky fixed income) I think determining the risky rate is a more purely additive process,
 
S2000’s explanation depends on the expected market return being constant and independent of the RFR. In other words, the RFR might go down but the market expected return stays the same. That’s a plausible assumption but by no means The only plausible one.
A different assumption, and the one that fits the OP’s question, is that the equity risk premium is independent of the RFR. The equity risk premium is how much higher the expected return on the market has to be (vs the RFR) to convince investors that it is worth taking on the risk of holding stocks, and it is not unreasonable to assume that this doesn’t change all that much of interest rates go up and down, because it is determined mostly by investors’ risk aversion, which (in theory) is independent of what the RFR is (though in practice is somewhat correlated because central banks often lower rates when fear is high).
The Equity Risk Premium (ERP) for s2000’s first scenario is 6% (8%-2%) and is 7% (8%-1%) in the second scenario. If instead, the ERP does not change in scenario 2, then the expected market return is 7% (=1% RFR + 6% ERP) instead of the 8% in s2000’s example. If the ERP is unchanged, you’ll find that all expected equity asset returns are 1% lower than they were in scenario 1, regardless of what the beta is, because beta*ERP doesn’t change in any of the equations.
in reality when the RFR is low, the ERP does appear to rise a bit, but perhaps not enough to compensate entirely. This is because low rates prompt some investors to “reach for yield,” most likely because they have discovered that they have insufficient assets deployed to meet their future liabilities and so start throwing Hail Mary passes.
Don’t use this dose of reality to answer a CFA exam question, though. Instead, look for evidence in the question as to whether the ERP is unchanged or the expected market return is unchanged. It will usually be one or the other, and they do like to make sure you are paying attention to the fact that the Market expected return is not the same as the ERP
 
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