# About Optimal Portfolio

Hi, I’m a bit confused while reading this part @ Volume 4 Portfolio Management On page 248, it says “The optimal portfolio is the efficient portfoio that has the highest utility for a given investor. It lies at the point of tangency between the efficient frontier and the (U1) utility curve with the highest possible utility.” Does that mean the Optimal Portfolio for a given investor always have to lie at the point of TANGENCY??? --> always the tangency point of envelope curve of efficient frontier and utility curve? I assume the so-called Highest Utility refers to the investor’s maximum acceptible risk level. From what I see at the graph of Exhibit 16 on page 249, Point X and Point Y seem not the only tangency points for the two groups of investors (risk-averse vs less risk-averse). I don’t know how our textbook confirms X and Y reprent the optimal portfolios for the two classes of invests??? The point Y does not even look like intersect the highest utility. Thanks for your opinion.

What is your objection to tangency? Are you thinking that an investor might be indifferent to any of a set of portfolios (you can create that and there’s some math conditions somewhere behind the statement that stop that).

No objection to tangency. From the Exhibit 16, it’s just not so clear to me why Point X and Y are selected as the optimal porfolio points. There could be more than one tangent points between those two curves, right? And the optimal one should be the point with highest utility value (risk tolerance point).

Sorry - don’t have books…

hyang: any point on the efficient frontier is the efficient portfolio… in exhibit 16 two points are picked to demonstrate the tangency… utility refers to how much risk investor is comfortable with … ----------------------------------------------------------------- Does that mean the Optimal Portfolio for a given investor always have to lie at the point of TANGENCY??? --> always the tangency point of envelope curve of efficient frontier and utility curve? ----------------------------------------------------------------- yes, bcoz the efficient frontier represents the best exp return portfolio for a given level of risk … look at the risk aversive investor utility functions … U1’, U2’, and U3’ … if you draw a drop down line passing through X and parallel to y-axis … U1’ return is less than U2’ and still investor has to take the same amount of risk, means U2’ the utility curve that is tangent gives better return for risk than U1’… and U3’ is not a possible combination of assets… though the utility function exists … think of it as — utility is what the investor is thinking and efficient portfolio is that is possible in market … for example an investor can have a utility function requiring 100% return and 0 risk … the utility function will be there but not possible to do so … read the efficient portfolio again and if you have schweser … read the construction of efficient frontier from schweser … and it will clarify a lot of things … again the two points chosen can be any two points … the author picked X and Y just to demonstrate…

Highest point of tangency = highest return, right. All portfolios below (to the left) are equally efficient but offer lower returns. The optimal portfolio on a risk adjusted basis offers more reward for an equal amount of risk. The further one moves along the frontier (to the right), marginal utility declines, returns level, the frontier flattens, therefore taking more risk is not necessary because theoretically there is nothing to gain by doing so. I guess mathematically where dx of the effecient frontier becomes zero or stops increasing is where you get your optimal portfolio. Somebody correct me if I’m off.

Thanks much for your explanation, madanalyst. Therefore, 1. For a given level of risk, there should be only ONE optimal portfolio, correct? 2. There could be more than one tangency points between efficient frontier curve and utility curve, right?

hyang Wrote: ------------------------------------------------------- > Thanks much for your explanation, madanalyst. > > Therefore, > > 1. For a given level of risk, there should be only > ONE optimal portfolio, correct? > 2. There could be more than one tangency points > between efficient frontier curve and utility > curve, right? Yes to both of your questions. With respect to question two, the multiple tangential lines just identify different rates of change at different points along the curve.