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Alpha Theory Blog - News and Insights

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1 posts from August 2009

August 5, 2009

Why do you buy an asset?



"We construct portfolios the way theory says one should, which is different from the way many, if not most, construct their portfolios.  We do it on a risk-adjusted rate of return.” – Bill Miller, legendary investor

Why do you buy an asset? Because you believe that it is worth more than what you are paying for it.

Assume you can buy two different assets for $20 dollars. Stock #1 is worth $35 and Stock #2 is worth $30, which one would you buy more of?

Of course, Stock #1 with a value of $35, because it is worth more. Unfortunately in investing, assets have risk. So, unless there is a 100% probability of the stock going from $20 to $35, you have to compare its upside potential to its downside risk to better understand how much return you are being paid for the risk you are taking on.

Assume we calculate the downside using net cash per share. Stock #1 has more upside to $35 but only $5 in net cash per share ($15 of upside and $15 of downside) and Stock #2 has a lower upside of $30 but more net cash at $15 per share ($10 of upside and $5 of downside). Now, which one would you take a bigger position in?


Stock #1

Stock #2




Current Price






Upside / Downside

$15 Upside / -$15 Downside

$10 Upside / -$5 Downside

More than likely you would have a greater exposure to Stock #2 because it has a better risk-reward. But this still misses a critical component of the analysis, conviction level. What if I’m extremely confident, say 80%, in Stock #1 achieving $35. For Stock #2, it is a coin-flip whether it will reach $30 or fall to $15. If I multiply each stocks’ Upside times the Probability of Upside and add it to the Downside times the Probability of Downside, I get a Risk-Adjusted Value of $29 for Stock #1 and $22.50 for Stock #2. The Risk-Adjusted Value is truly representative of the full qualities of this asset and should be the basis from which portfolio level decisions are made.



Stock #1

Stock #2


$35 * 80%

$30 * 50%

Current Price




$5 * 20%

$15 * 50%

Probability-Weighted Return

$29.00 / 45%

$22.50 / 12.5%

If you were to invest in Stock #1 10 times, you would make $15 eight times and lose $15 twice for a total gain of $90. If you were to invest in Stock #2 10 times, you would win $10 five times and lose $5 five times for a total gain of $25. Now, which asset would receive greater exposure?

Every investment decision should be framed by Probability-Weighted Return. This allows an investor to properly size positions and quickly adjust exposure as the underlying price of the asset changes and as new fundamental information is received. Although the concept seems simple, it is rarely implemented. To see how Alpha Theory puts this concept into practice, view our demo (www.AlphaTheory.com/demo).