Let’s say we have an investor who’s going to invest in a portfolio that includes two stocks, we’ve got stock A and stock B. This investor can invest in any different number of combinations. They could put 90% of the portfolio in stock A and then 10% in stock B or they could do 80/20, they could do 10/90. They can do any number of combinations and so we can go and we can plot different points and then we can draw a graph we can graph those points and this is showing the different volatility and expected returns for different weights of this portfolio. We could have more than two stocks but I’m just gonna keep it with two stocks just to make it simple.
So we’ve got A and B, all these different points are different combinations or different weights of stock A and stock B in this portfolio. Let’s say we take the point of 10/90. 10% in stock A and 90% in stock B. So we say that the portfolio has volatility of 15% and then able to expect a return of 5%. All of the ones on this yellow part, these are inefficient portfolios. So these are inefficient and when I say inefficient I mean that we could find a different portfolio that has a higher return yet does not have a higher risk, it has the same volatility but a higher expected return. So obviously then we would say we don’t want this portfolio because we can get a higher expected return without taking on any more risk. So all these ones they’re yellow are inefficient and then all the ones that are on the purple line here these are all efficient portfolios.
Now let’s say that the risk-free rate of return is 4% which is one month of treasury bills or something like that hypothetically. So this is the risk-free rate of return that’s 4%. Now from that risk-free rate of return, we could draw a line, we could draw a line such that it’s tangent and such that it barely touches this purple line. By the way, there’s the purple part, that’s called the efficient frontier. So the part where this line touches the efficient frontier. We’ll say this is the tangent portfolio where this line touches and so this red line is called the capital market line.
There’s going to be a lot of information here. That’s the tangent portfolio when I say tangent it’s a portfolio just where the curve touches that red line which is the capital market line. Then If the assumptions of the Capital Asset Pricing Model (CAPM) hold that is also going to be the market portfolio. By the way, this red line is the capital market line, which has all the different combinations we could have. So is this is different weightings of stock A, stock B, and the risk-free asset. So that what the capital market line is different than the curve. The curve is just different combinations of stock A and stock B but in the white line, we also added in the risk-free asset. So it’s the tangent portfolio, it’s the market portfolio and it’s also that portfolio with the highest Sharpe ratio.
I have another article where I wrote about the Sharpe ratio specifically but basically, it’s we’re thinking about the excess portfolio return divided by the volatility. So we could think about it as a reward for volatility. Remember volatility is a total risk that’s the standard deviation of the stock returns. So in terms of the reward to volatility, the highest reward per unit of volatility is the most bang for your buck in terms of we’re taking out a certain amount of risk and how do we get the highest reward. If we’re thinking of ranking portfolios, the one with the highest Sharpe ratio is the one that gets the highest reward given the volatility.