Q. In the current interest rate environment, using a required return estimate based on the short-term government bond rate and a historical equity risk premium defined in terms of a short-term govt. bond rate would be expected to :

bias long-term required return on equity estimates upwards.

bias long-term required return on equity estimates downwards.

have no effect on long-term required return on equity estimates

In volatile IR environment historical equity risk premium may not hold what would bias short-term required return on equity. However, the situation does not affect long-term required equity return.

The required return reflects the magnitude of the historical equity risk premium, which is generally higher when based on a short-term interest rate (as a result of the normal upward sloping yield curve) (why?), and the current value of the rate being used to represent the risk-free rate. (what does this mean?). The short-term rate is currently higher than the long-term rate, which will also increase the required return estimate. The short-term interest rate, however, overstates the long-term expected inflation rate( how and why?) . Using the short-term interest rate, estimates of the long-term required return on equity will be biased upwards.

In a normal upward sloping yield curve, shorter-term maturities have lower yields, which means, the risk-free rate is lower. Equity Risk Premium = market returns minus risk-free rate. If we use a lower risk-free rate, then our equity risk premium must be higher, all else equal, because we are subtracting a lower amount.

This is just saying that the risk-free rate used to calculate required returns is that short-term rate.

The question says the yield curve is presently inverted, ie, the short-term rate is higher than the long-term rate, so the first sentence is just a reflection of that. The question says that short-term inflation rate is 7%, but long-term inflation rate is 4%; short-term yields are 9% and 10-year maturities are 7%. So, it is saying that the short-term rate is based on a temporarily higher inflation rate, hence, the short-term rate is overstating the longer-term expected inflation rate of 4%.

Accordingly, if we used the short-term interest rate as our risk-free rate, then any estimate of long-term required return will be biased upwards (because in the long-term, the risk-free rate will be smaller presumably because the expected inflation rate is smaller). The key is to understand the effect of the yield curve on the required return.

We have Required risk premium = Req rate of return - RiskFree rate. ; Req return = RiskFree + BETA (Market premium)

So we have a high RF rate (9%) meaning that Market premium is LOWER, then for Req. Return, the RiskFree is higher + a lower market premium TIMES A BETA and we don’t even know the beta. So how can we even answer this question?

Ignoring BETA, the required rate be HIGHER because since the RiskFree is higher, the effect of a higher RF should be stronger than of a lower market premium, so is this the rationale?

I don’t like the way this thing is worded and it’s confusing as hell!

the CAPM (that use Beta) is just one way to determine the required return, and is generally used, but in this question you don’t have to think about beta, this is more like a build up method (where you add risk premium to the risk free) and id the yield curve is inverted (higher risk free in short term) the required return will be biased upward cause you are using a higher rate to build for that required return

Question says “government yield curve is inverted; at the short- end, yields are 9 percent and at 10- year maturities, yields are 7 percent.” The geometric mean return relative to 10- year government bond returns over 10 years is 2 percent per year.

What will happen if we use short- term government bond rate and a historical equity risk premium (2%) in calculating long term required return?

Since we are using short term government bond (9%) as Rfr for CAPM, the Required Rate of return is higher compared to using long term government bond (7%). Upward biased.

Historical Equity Risk Premium is 2%

Conclusion, by using short- term government bond rate and a historical equity risk premium will lead to upward biased estimation of long term required return on equity.