Portfolio risk budget

1. Portfolio risk budget

Let’s end this chapter with a who did it game,

2. Who did it?

called risk budgeting. It tries to answer the question about how much of the portfolio risk is caused by each of the

3. Who did it?

individual portfolio positions. This is not just for fun, but it is now common practice for portfolio managers to identify the sources of portfolio risk and to avoid that the portfolio risk is too concentrated in a few assets. This slide visualizes what we will be doing. It shows on the left an example of a capital allocation budget saying how much of the wealth is invested in each asset. On the right, it shows how much of the portfolio volatility risk is caused by each of those assets. The figure on the right is called the risk budget. As you can see, the capital allocation and the risk allocation can be very different. The reason is that the portfolio volatility does not only depend on the weights, but also on the assets' volatilities and their correlations. So, practically,

4. Portfolio volatility in risk contribution

how do we obtain such a risk budget? The first step in constructing the risk budget is to rewrite the portfolio volatility as the sum of the volatility risk contributions of the N portfolio positions. I show the corresponding mathematical formula on the slide, but in the exercises, we will see the functions that implement this in practice. The risk contributions add up to the total portfolio volatility. In order to have an estimate of the percentage risk caused by each of the N portfolio

5. Percent risk contribution

positions, we will take the risk contribution of that position and divide it by the total portfolio risk. This ratio is called the percentage risk contribution. Let's now play the who did it game in the case of our asset allocation problem. Because investing in stocks is more risky than investing in bonds, you will see that the percentage risk contributions of the position in stocks is much larger than its portfolio weight, while for bonds, it is the opposite.

6. Let's practice!

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