Derivatives
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š Why Long-Term Stock Guarantees Are More Expensive Than They Look I recently came across a fascinating āBusiness Snapshotā in John Hullās classic textbook Options, Futures, and Other Derivatives. It deals with a question many investors assume has an obvious answer: āIf you invest for the long run, arenāt stocks guaranteed to outperform bonds?ā Hull…
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Microsoft was one of the first companies to grant stock options to all employees. Later it was estimated that thanks to this decision, more than 10,000 employees became millionaires. Stock-based compensation is still actively used today. It used to be even more popular because it helped attract valuable employees without appearing as an expense on…
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How to Assess a Stockās Risk Based on Historical Data We know that in finance, āriskā usually refers to volatility, i.e., uncertainty regarding changes. Here, I want to highlight a few important points. The volatility (Ļ) measure is very commonly used in practical finance when we: It is therefore important to understand clearly what this…
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Suppose an investment fund (or a development company) promises you an average return of 14% per year. To convince you, they show that over the last 5 years their returns were: 15%, 20%, 30%, ā20%, and 25%. The average of these is indeed 14%. Does the promise sound credible? Letās check mathematically. The promise:A 5-year…
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Why diversification fails during market crisesā¦ Assume two variables, (x_1) and (x_2), follow generalized Wiener processes: dx1 = a1Ā·dt + b1Ā·dz1 and dx2 = a2Ā·dt + b2Ā·dz2 The corresponding discreteātime versions of these continuous processes are: Īx1=a1*Īt+b1*Īµ1*Ā āĪt įį Īx=a2*Īt+b2*Īµ2*Ā āĪt If we assume these processes are independent, then Īµ1 and Īµ2 are simply standard normal random…