# Tim Swan Case (Asset Allocation and Related Decisions in Portfolio Management)

Q3:

Based on Exhibit 2, the ratio of the excess return to the marginal contribution to total risk (MCTR) of the portfolio is closest to:

A is correct. Because the portfolio is optimal, the ratio of the excess return to the marginal contribution to total risk (MCTR) is equal to the Sharpe ratio for the portfolio:

Wouldn’t the Excess return of the portfolio/MCTR always be the sharpe ratio?

I mean the marginal contribution to total risk of the whole portfolio is equal to the standard deviation of the portfolio returns, isn’t it?

no, MCTR of an asset class to the portfolio is the asset beta x portfolio std deviation.

yes. but MCTR of the whole portfolio is portfolio beta against itself (=1) times standard deviation of portfolio.

yes that’s sharpe ratio, and?

my point is that the answer’s reasoning “BECAUSE the portfolio is optimal” is not necessary.

New year, same doubt on this question.

I’d essentially agree with EuroBill. Opinions?

Excess return to MCTR of the whole portfolio is the Sharpe ratio of the portfolio - what we calculate in this question.

(9.5 - 1.8) / 21.63 = 0.356

Yes, MCTR of the whole portfolio is 1 x st. dev. of the whole portfolio.

I agree “because the portfolio is optimal” does not make too much sense here.

Below rewording might make more sense?:

Unless the portfolio is optimal, it’s (Portfolio’s) sharpe ratio won’t be EQUAL to marginal contribution of (the asset class’s risk ) to total risk

Yes yur rephrasing is correct (if I get it well):

The portfolio is considered optimal, when its Sharpe ratio equals the ratio of excess return to MCTR for each of the porfolio constituents.

If the portfolio was not optimal, its Sharpe ratio would not equal the ratio of excess return to MCTR of each of the constituents.

But still the calculation would be the same.

Calculate the excess return to MCTR for each of the 4 portfolio constituents all is 0.356 just as the Sharpe r. of the portfolio.

This is a much more simple question than the time we spend on it.

only optimal portfolios have ER/MCTR = SR