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I am currently reading John C. Hulls' "Risk Management and Financial Institutions" and came across the following passage related to the efficient frontier and combinations of risky and risk-free assets:

It is a short step from here to argue that the portfolio of risky investments represented by M must be the portfolio of all risky investments. Suppose a particular investment is not in the portfolio. No investors would hold it and its price would have to go down so that its expected return increased and it became part of portfolio M. In fact, we can go further than this. To ensure a balance between the supply and demand for each investment, the price of each risky investment must adjust so that the amount of that investment in portfolio M is proportional to the amount of that investment available in the economy. The investment represented by point M is therefore usually referred to as the market portfolio.

The following part confuses me:

No investor would hold it and its price would have to go down so that its expected return increased and became part of portfolio M.

This makes little sense to me at the moment. I understand that by excluding a particular investment (say $I$) in $M$, its demand will decrease as all risk-adverse investors will purchase portions of $M$ to produce a linear efficient frontier. This will decrease the price of $I$ but I am not sure why this will increase its expected value, and thereafter be inserted into the market portfolio.

I am also confused about the proportions part of the passage.

Any help would be truly appreciated.

Thank you

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    $\begingroup$ Assuming a security will produce positive cash flows in the future (i.e. assuming it is not just a useless piece of paper), then lowering today's price will increase the future expected return. $\endgroup$
    – nbbo2
    Feb 10, 2016 at 13:59
  • $\begingroup$ @noob2. When I think of expected return, I think of that defined by the Capital Asset Pricing Model. I cannot connect a decrease in price with an increase in expected return of an asset. $\endgroup$
    – Gustavo Louis G. Montańo
    Feb 10, 2016 at 14:55
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    $\begingroup$ Why not? Under CAPM the current price is equal to the present value of the cash flows discounted at the rate $R_f+\beta(R_M-R_F)$. This is the essence of the CAPM: if the price is too high it has to drop until this condition is satisfied. $\endgroup$
    – nbbo2
    Feb 10, 2016 at 15:04
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    $\begingroup$ So the CAPM is the equilibrium condition, and the price adjusts up or down until the condition is satisfied. It is this adjustment process that Hull is describing. $\endgroup$
    – nbbo2
    Feb 10, 2016 at 15:26
  • $\begingroup$ Ahh I see! This was the perspective I was missing. Thank you @noob2. However, I am now having trouble understanding why the increase in expected return would entitle investment I into portfolio M. I understand that if its expected return increases (and so will its standard deviation), it will move along the set of points $\left(\mathbb{E}(R_{i}), \sigma_{i}\right)$. However, how can we be sure that investment I converges into portfolio M (if that's the point of the exercise). Can't investment I move to the "right" of portfolio M? $\endgroup$
    – Gustavo Louis G. Montańo
    Feb 11, 2016 at 0:34

1 Answer 1

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First understand that following proposition are based on CAPM.

To understand how price and expected returns are related you can read following answer. It answer to different question but example describe in this answer will let you to understand how both are related to each other.

Now come to your second confusion

.....that the amount of that investment in portfolio M is proportional to the amount of that investment

First focus what is market portfolio under CAPM?

Market portfolio is sum over, or aggregate, of the portfolios held by each individual in the economy. Lending and borrowing will cancel out (because each lender has a corresponding borrower), and market portfolio will comprise only the value of the aggregate risky portfolio, equal to the entire wealth of the economy.

CAPM assumes each investor hold similar portfolio i.e. market portfolio. So each investor hold same proportion of every security in their portfolio. This means that if the weight of Wipro stock in each common risky portfolio is 1%, then Wipro also will constitute 1% of the market portfolio (common sense).

This is the same thing that author want to convey from his statement.

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  • $\begingroup$ Ahh I understand. Thanks! However, I am not sure what you mean by "Lending and borrowing will cancel out". If every lender has a borrower then certainly borrowing and lending exist. In addition to the former confusion, while I understand the relationship between decreases in price and expected return, I am unsure on how it implies that the market portfolio consists of every risky investment. Please read my comment on the original question for elaboration. $\endgroup$
    – Gustavo Louis G. Montańo
    Feb 11, 2016 at 1:29
  • $\begingroup$ @GustavoMontano If you sum portfolio of each and every investors, then borrowing and lending will cancel out each other and you will left only with the risky assets. All propositions are just based on CAPM assumptions. $\endgroup$
    – Neeraj
    Feb 11, 2016 at 14:24

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