Trick Question? - Which Stock is riskier?
Warning: I'm a layman when it comes to finance (I'm an Engineer). I was wondering if this is just a simple question or if there are deeper insights.
"Stock A trades at $10/share and has a beta of 2.0; stock B trades at $50/share and has a beta
of 0.5. Suppose you know with perfect knowledge that both stocks are worth $55/share, which one is
riskier?"
Seems to me that since Beta is higher for A, it would be considered riskier. However, the price is so much lower, you would not need to put down as much money to reap the same returns.
Stock A is underappreciated by %550, while B is underappreciated by %110. You'd only have to invest 5 times less in Stock A to receive the same returns if the prices started to return to their true value. The question is: does that mean it is simply has more potential, or does that factor into it's perceived risk?
If you can see the future and know that both shares is going to be worth $55/share, then there are no risk. Personally I think risk is a misnomer, it should be uncertainty. Risk can be quantifiable, uncertainty isnt.
I don't think the question means "seeing the future", just knowing the true value of the stock. Even if the value is $55, isn't there a risk/uncertainty that the rest of the market (which contains a great number of irrational people) won't actually value it correctly?
I'd just keep buying the $10 stock til I own it all, then I'd be rich.
Beta only measures systematic risk and is assumed to measure a stock's overall risk only under the assumption of a perfectly efficient market. If you know, with perfect knowledge (I'll assume that means no insider information), that stock A is worth 5.5 times its market value, then the market isn't efficient. So beta isn't capturing unsystematic risk in this case and isn't very useful. Additionally, beta is backward looking and your valuation is forward looking.
And if the assumption that over time the market value converges with intrinsic value, I would say that stock B is riskier. We would expect Stock A's returns to be more rightward skewed than Stock B's because of that convergence. I think lower partial moment might be more relevant than beta for this stock.
Or something along those lines...
All else equal, stock A is riskier. If you are a buyer, price appreciation to $55 would be upside risk, which is still considered risk even though the term is generally used for downside.
If you "KNOW" the stock price is worth 55 AND you know it will actually appreciate to 55, neither stock has any risk if you pay cash for them if you can hold to the date it realizes fair value. Stock A is clearly a better buy though (all else equal). It would help to know the timing of when it would realize that value. If you know stock B will hit 55 tomorrow, but stock A will hit it in 10,000 years, I'd take stock B.
Edit: The trick in this question is claiming to "know" anything about what the future holds. There are only probabilities.
I think you could also think about it in terms of expected returns per unit of market risk - i.e. expected return/beta (not a technically correct formula, but close since - Expected Returns - Rf / Beta = slope of securities market line).
Even if you assume the same end point in time, and that both stocks will go to $55, you may have different paths to get there (the volatility of the stock). The beta describes the behavior of this path relative to the market. Stock A has a much higher ratio, and should be considered to have a greater return-to-risk reward. Hence, I would consider this less risky.
I agree with the idea of a risk/reward ratio, but I would think that a Sortino ratio or Kelly Criterion would be more relevant because we would be worried more about the rightward skewness of Stock A's returns than the even bidirectional distribution assumed by the CAPM.
Unless Stock A has more default risk than B (which seems unlikely given their equal intrinsic value), Stock A would be less risky when you take its lower partial moment into account. Same conclusion, though.
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