Question

1. Chicken McSpirkle is an eccentric who has developed an asset pricing model. Like generally accepted pricing models, Chickens model predicts a relationship between risk and expected return. However, Chickens model uses something called Zarumba (represented by the variable Z in Noodles’ writings) as a risk measure. No one but Chickens understands how to calculate Zarumba, but Noodles claims to have proven that, for any stock, E(R) = 3Z. The following table provides data for five stocks, including actual return, Zarumba, and beta.

Stock	Zarumba	Beta	Actual Return
A	0.08	2.00	32.0%
B	0.24	1.75	32.0%
C	0.07	1.20	24.0%
D	0.04	0.50	12.0%
E	0.03	0.25	8.5%

1. For each stock, calculate the expected return according to Chicken model and the CAPM. The expected return on the market is 20%, and the risk-free rate is 4%.

2. For each stock, use both pricing models to determine whether or not the stock earned an abnormal return.

3. What does this problem reveal about the real-world difficulties of determining whether or not the market is efficient?

Answer 1

Chicken Mcspirkle

Calculation of Returns

Given

Risk free rate =Rf=4%

Expected Market Return=Rm=20%

Let the Retuen of Stock be Re

Ans i
Stocks	Beta	Return as per CAPM : Re=Rf+beta*(Rm-Rf)	Zarumba	Return using Zarumba : E®=3*Zarumba%	Actual Return	Difference of Actual return with CAPM return	Difference of Actual return with Zarumba return
A	2	36.00%	0.08	24.0%	32%	-4.00%	8.00%
B	1.75	32.00%	0.24	72.0%	32%	0.00%	-40.00%
C	1.2	23.20%	0.07	21.0%	24%	0.80%	3.00%
D	0.5	12.00%	0.04	12.0%	12%	0.00%	0.00%
E	0.25	8.00%	0.03	9.0%	8.5%	0.50%	-0.50%

Ans ii
From the above table it is clear that there is abnormal difference in stock A against actual result by CAPM methos.
In Zarumba methos, there are abnormal returns in stock A, B & C against actual result. The result of stock B is particularly
abnormal by a great degree.

Ansii
It is difficult to determine whether the market is efficient. The return for a stock should be proportional to the risk
associated. Here both stock A & B giving 32% return , but their beta are different and the Zarumba factors are hugely
different . So it is not clear of the market is effcient to reflect their risk factors.