Active risk is the level of dispersion that an active manager would bring compared to their passive benchmark, so the benchmark that they're trying to outperform. So it's really the level of additional volatility associated with excess returns, excess returns being the return from the active portfolio manager compared to the benchmark. Normally we proxy active risk by looking at the standard deviation of excess returns, and that is called a tracking error.

Of course, that's not the only metric and tracking error, so the volatility of excess return, can be related not just through stock picking or market timing, so it might not just come from the intrinsic outperformance of the active manager and their level of skill, but it might also come from implicit exposures that an active manager might have, like factor exposures.

That's really the key metric that we use in order to assess the level of risk that managers would bring in a portfolio that has both active and passive.

Active risk tolerance is the level of active risk that an investor is willing to take into his or her portfolio that has more active exposures than passive exposures. Along with the expected alpha and the level of active risk, proxied by tracking error, is the third metric that we use in the active passive framework to identify the optimal blend between active and passive in an optimised portfolio.

I would say that all else equal an investor that has a higher level of active risk tolerance would lead to a portfolio that has an active passive mix that is higher, so it could be as high as a 70, 80 or even 90% of their exposures being taken through active portfolio managers. An investor instead that has a lower active risk tolerance would probably be an investor that has most of his exposures in passive funds.

At Vanguard, we use a quantitative model in order to provide the optimal blend between active and passive. The model that we use is the Vanguard Asset Allocation Model, abbreviated into VAAM, and that's really a quantitative model that is based on what we call a maximisation expected utility, which is a sophisticated way of saying that we take into account the tradeoffs between risk, returns and tolerance towards those risks for any given investor. That means taking into account the expected alpha that we talked about, the tracking error, the implicit factor exposures that active managers would bring, the active risk tolerance, of course, and also our capital market assumptions. So those are modelled with the Vanguard Capital Market Models, abbreviated into VCMM, and this is the tool really that forecast our expected returns into the future for different asset classes and sub asset classes.

All this would be input into VAAM, which then provide the optimal asset allocation between sub asset classes and active passive blending.