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The Power of Diversification: Understanding Risk and Reward in Investing

Explore the concept of investment diversification, inspired by Warren Buffet's quote highlighting the need for understanding over spreading risk blindly. This module covers key principles such as information ratio, information coefficient, strategy breadth, and the Fundamental Law of investing. Learn why making numerous small bets can be more advantageous than a single large one by examining case studies that compare reward/risk outcomes. Discover the mathematical underpinnings of risk assessment through practical examples, and understand how to optimize your investment strategy for better returns.

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The Power of Diversification: Understanding Risk and Reward in Investing

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  1. Motivating Quote “Wide diversification is only required when investors do not understand what they are doing.”  – Warren Buffet

  2. Module Objectives • Understand information ratio (IR) • Understand information coefficient (IC) • Understand strategy breadth (BR) • Understand the Fundamental Law • Learn why lots of small bets are better • Learn about example applications of the Law

  3. A Thought Experiment • Stock trade = Bet • Coin flip = Bet • Uncertainty = Beta • Coin bias = Alpha • 51% heads

  4. Conditions of One Bet • We bet one token • Win: Now own two tokens • Lose: Now own zero tokens

  5. What if We Make Multiple Bets In Parallel? • Case 1: • One bet with $1,000 token • Case 2: • 1,000 bets with $1 tokens • Which is better?

  6. Consider Reward/Risk • Reward = expected return • Single bet case: • 0.51*1000 + 0.49*-1000 = $20 • Multi bet case: • 1000 * (0.51*1 + 0.49*-1) = $20

  7. Consider Reward/Risk • Risk measure 1: Possibility to lose everything • Single bet case: 49% • Multi bet case: • 0.49 * 0.49 * 0.49 … * 0.49 = 0.49^1000 (small!)

  8. Consider Reward/Risk • Risk measure 2: standard deviation • Multi bet case: • STDEV(1, -1, 1, -1, 1, 1, …, -1) = $1.00 • Single bet case: • STDEV(1000, 0, 0, 0, 0, …, 0) = $31.62

  9. Consider Reward/Risk • Single bet case: • Reward/Risk = $20 / $31.62 = 0.63 • Multi bet case: • Reward/Risk = $20 / $1 = 20.0 • Same as Sharpe Ratio

  10. Observe • SR(multi) = SR(single) * SQRT(1000) • 20 = 0.63 * SQRT(1000) = 0.63*31.62 = 20 More generally: • SR(multi) = C * alpha * SQRT(bets)

  11. Observe • Same expected return, but • Multi bet case: • Much lower risk to lose everything • Much lower standard deviation • Much higher reward/risk ratio

  12. Take Home Lessons • Higher alpha = higher Sharpe Ratio • More bets = higher Sharpe Ratio • Sharpe Ratio grows as the SQRT of brea

  13. Motivating Quote “Wide diversification is only required when investors do not understand what they are doing.”  – Warren Buffet

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