Hello, in the last lecture we reviewed how to measure the risk of an individual asset. Let's now continue our discussion of finding a measure of portfolio risk. Specifically, let's consider again a portfolio that is 50% invested in Toyota and 50% invested in Pfizer and find it's volatility. Okay, so you remember this table from the previous lecture, right? In the previous lecture we found the return to this portfolio in each state of the economy, and now we also found this expected return which we found to be 3.275%. Okay, so now we can find the variance of that return around this expected return by computing it, probability weighted average of the square deviations from this mean, right? So let me write that down, right? What is the variance? What is the portfolio variance? I'm going to call that sigma squared p, right? It is the probability weighted of the square deviations from the mean, right? So, 0.1 x (4.25- the mean) squared, plus the probability of normal times the outcome minus the mean squared plus 0.3, the probability of a recession, the outcome, the return in that state minus the mean. Finally 0.2 the probability of the depression, 5% minus the mean, all right, squared. And if you all do that, you're going to find that the variance of this portfolio that is 50% invested in Toyota and 50% invested in Pfizer is 1.66. If I take the square root of that, that's going to give me the volatility of that portfolio, that's going to be 1.29%. Okay, so the volatility, right, an equally weighted portfolio that consist of Toyota and Pfizer, is 1.29%. But wait a minute, how did that happen, right? We combined, in equal ways, an asset with a volatility of 4.02%, and another asset with a volatility of 5.11%. And we got a portfolio with a volatility of only 1.29%, right? Clearly 1.29% is not the weighted average of these two volatilities. It's way, way less, all right? So what's going on here? Well like I said before, the volatility or the variance of a portfolio is not simply the weighted average of the individual asset variances. Okay, so to understand this, let's look at this a little more closely in the next lecture.