Hi, guys. I feel stupid when reading the section 2.6 about risk budgeting.
Textbook states:“Finally, an asset allocation is optimal from a risk-budgeting perspective when the ratio of excess return (over the risk-free rate) to MCTR is the same for all assets and matches the Sharpe ratio of the tangency portfolio.”
I think this statement is meaningless. We know:
MCTR=beta i * portfolio standard deviation;
Excess return=expected return i - Rf = beta i * Portfolio Risk Premium
Thus, Ratio of excess return to MCTR= Portfolio Risk Premium / Portfolio standard deviation , which is the Sharp ratio of portfolio and this rate is definitely fixed in this example. Once we know the weighting of each asset, no matter what it is, you are absolutely going to have an identical ratio of excess return to MCTR, even it is not an optimal asset allocation.
The whole segment on MCTR feels a bit rushed and poorly explained to me.
I might be completely wrong on this, just making an attempt to make sense of it. Let me know your thoughts.
What I think it is, is that Excess Return of an asset class is based on Beta w.r.t the market portfolio, whereas the Beta used in MCTR is Beta with respect to the portfolio in question , so they are different betas, which means they don’t cancel out to equal the portfolio Sharpe in the way you described.
This makes sense to me, as the expected spread of an asset class to the risk-free-rate is not going to be based on anything in the individual’s portfolio, it will be based on the MRP* B(i,m) - RFR .
The Beta(i,p) used in MCTR is different and is influenced by Asset Class selection, CFAi state on P267 “Critically, beta takes account not only of the asset’s own volatility but also of the asset’s correlations with other portfolio assets.”
It’s more confusing, because in the CFAi notes they use the Portfolio Betas from the Reverse Optimization in Exhibit 12 for the MCTR example. Reverse Optimization uses an estimation of the market portfolio in order to discover market expected returns, so in the case of the CFAi examples , both Betas are the same, but in a case where your asset allocation didn’t comprise of the entire market portfolio, they could be different.