A regression is run for each of 3 stocks in which the Y variable is the monthly

Question

A regression is run for each of 3 stocks in which the Y variable is the monthly return on the stock and the X variable is the monthly return on a market index. The data are coded in decimal form, meaning that a 5% return would be 0.05 in the data. It can be assumed during this period that the monthly risk-free rate was 0%. The regression results look like this:

Stock 1

Y = 0.0139 + 1.52X R-square = 0.15

Stock 2

Y = -0.0054 + 1.19x R-square = 0.47

Stock 3

Y = 0.002 + 1.60x R-square = 0.23

Which stock earned the highest return during the historical period over which you estimated these regressions?

Assuming the Capital Asset Pricing Model (CAPM) is true, which stock has the highest expected return in the future?

One of these firms is a diversified conglomerate, and the other two operated only in one or two lines of business. Which is the conglomerate and why?

Explanation / Answer

Intercept is what gives us the returns that stocks make when market returns are zero.

Stock 1 has the highest intercept at 1.39%

There's a formula for calculation how much better stock has performed relative to market in the past.

It is given by Excess Past Return = Intercept - Riskfree rate * (1 - Beta)

In this case Riskfree rate is zero so we can safely say that stock with highest intercept gave highest return wrt the market.

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According to CAPM model, Expected Return = Riskfree rate + Beta * (Market rate - Riskfree rate)

Riskfree rate = 0% ( given)

Expected return = Beta * Market rate

The co-efficient of X gives the slope of the equation ie it tells us how Y changes per unit change in X.

This is similar to how Beta gives us volatility wrt the market.

Since Stock 3 has the highest co-efficient, it will give the highest returns as per CAPM model

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Proportion of risk that is diversifiable in a company is given by 1-R2

In case of stock 1 this value is the highest at 1-0.15 = 0.85

So stock 1 is the diversified conglomerate.

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