Bifalgorithm post

Can we use maths to reduce the risk of investing in stocks? Yes, and let me show you how. Imagine putting all your money into just one stock. Its return is uncertain. Sometimes it goes up, sometimes it goes down. As a simple model, suppose its return follows a normal distribution with mean, mu, and standard deviation, sigma. The the portfolio has expected return, mu. So diversification hasn't reduced our expected return. But now look at the volatility. Suppose each stock has the same standard deviation, sigma, and their returns are independent. The variance of our average becomes 1 over N squared multiplied by the sum of the individual variances. Each variance is sigma squared and there are n of them. So the portfolio variance simplifies to sigma squared over n. Taking the square root gives a portfolio standard deviation of sigma over the square root of n. And that's the key result. With one stock, volatility is sigma. With four independent stocks, it falls to sigma over two. And with sixteen, it falls to sigma over four, a 75% reduction. Visually, the distribution gets narrower and narrower around the same mean. But there's an important catch. Real stocks aren't independent. A recession, financial crisis, or market panic can hit many companies at the same time. The real challenge isn't simply owning more stocks. It's owning assets whose returns don't all move together. Follow for more Maths animations.

Can we use maths to reduce the risk of investing in stocks? Yes, and let me show you how. Imagine putting all your money into just one stock. Its return is unc…