CML and point of tangency with market portfolio

[Eustice_Langham]

Hi, There is a quote in the Kaplan materials that I hope someone can clarify for, the context isa discussion of the CML and point of tangency with the market frontier:

"At any point to the left of M, investors are lending at the risk-free rate because some of their money is invested in Treasuries, whereas at points to the right of M, they are borrowing at the risk-free rate (i.e., using leverage to magnify their investment in the market portfolio)."

My question is at any point other than the point of tangency, why is the investor lending ie the left and borrowing to the right of the point of tangeny?

 

[nc27]

Consider a world where you can only invest in two securities.

1) The riskfree security yields the riskfree rate (for example a treasury bill)
2) A risky security which yields the market portfolio returns. Market portfolio is a portfolio consisting of a weighted sum of every asset in the market, with weights in the proportions that they exist in the market . For example, to represent a type of market portfolio, think about the S&P500 index, which yields the weighted average returns of 500 US companies.

Now, if you can invest your money only in these two securities you will either:

a) invest all your money in the riskfree security (the RF point on the y axis of the graph)
b) invest all your money in the risky security (the M point on the graph)

OR

c) invest your money in the riskfree security and the risky security (on the graph you are on the left of the M point that represents the market portfolio). That way, you are certain that you will get a riskfree return as you have invested part of your money in the riskfree asset.

d) invest all your money in the risky security and borrowing more money from the bank that will charge you the riskfree rate (on the graph you are on the right of the M point that represents the market portfolio). That way, you leverage your position (i.e. you invest more money that you originally have in your account) and you hope that you will get a higher return by investing it all in the risky asset (do not forget you will have to pay back to the bank the borrowing plus the riskfree interest rate that is being charged to you).

 

[Eustice_Langham]

Thanks for the thorough response.

My question however is why does being either to the left or right of point M mean that as an investor you are either lending (ie to the left of point M) or alternatively to the right of point M you are borrowing. Is it as simple as at point M you have fully employed all resources thereby if you are to the left or right you are either under employed to the left or over employed to the right of point M?

 

[nc27]

Yes as you mention,

For the first point, on the left of the point M, you are lending money. Maybe your confusion is on the use of the term "lending". Why do I lend money if I invest my money in two securities (riskfree and risky)?. Well, as I see it, when you invest your money in riskfree assets (money market instruments (i.g. treasury bills) or fixed income instruments (i.g. bonds)) you are lending your money to the government. That is why you get a yield equals to the riskfree rate (i.e. your compensation for investing in riskfree assets, or equally, lending your money to the government).

For the second point, as mentioned earlier, on the right of the point M, you are borrowing money at the riskfree rate (from some bank). So you get the opportunity to invest more cash in the risky market portfolio asset (you will get a higher yield but at the cost of a higher risk (measured by the volatility of returns of the market portfolio).

This simplified view of the world is not realistic of course, if you want to know more about the subject look at markowitz portfolio theory and the two fund separation theorem on the web.

 

[sulemanms202]

Dear nc27.. Risk free assets i'd assume are for covering unsystematic risk since beta covers systematic risk. But i cant seem to understand how does portfolio come in the understanding when we start with the assumption of short selling?

and for instance we have a bank which finances purchase of raw material for a company. If i buy bank's shares wouldnt that cover both syst and unsyst. risk?