portfolio risk measures recap Now back in module one, we had extensive conversations around risk and risk and portfolios in volatility was a key component of that discussion and that's because volatility is the most popular way of measuring and expressing risk in Investments and in portfolios, so risk and therefore volatility is an indication of how variable the outcomes could be. And in fact a modern portfolio Theory incorporates volatility into its analysis and the higher the risk or volatility the higher the required return by investors from Investments or portfolios. Now, I'll portfolio Theory equates to risk with volatility. It's important to note that some will argue that risk and volatility are not synonymous rather that volatility is just a measure of one type of risk, and that's because volatility is not perfect for several reasons.

First of all volatility is non-directional. So it measures both upside.

Downside volatility and most investors are just concerned with a downside risk or downside volatility also volatility can underestimate actual risk, because we're using historical data and historical data might not be the best predictor of future volatility. Now, how is portfolio risk or volatility calculated? Well again volatility or risk number is defined by the varying degree of prices over a period of Time how widely do outcomes vary and in module one, we discussed two key measures standard deviation and variance and these two measures do exactly that they measure the variability of outcomes, but we can't stop there because remember we're not talking about single Investments. We're talking about portfolios. So not only do we need to measure the variability of each underlying holding. We also need to get a sense of how the assets move together and then we talked about correlation and covariance that measure whether acids tend to move.

Together or in the opposite direction or don't move together at all. Again. These measures were all discussed in detail in module one, but we think it's important to review them here again in the following videos.