Two-Fund Separation Theorem
Correct!
If you have a risk tolerance less than that of the market portfolio, then your optimal portfolio can be expressed as a mix of the risk-free asset and the market portfolio. Your portfolio in this case is called a lending portfolio. By putting a portion of your assets in the risk-free asset, you are doing the equivalent of placing some of your money in the bank. These funds may ultimately be lent out to others.
Modern Portfolio Theory suggests that investors select optimal portfolios based on a match between their risk tolerance and the efficient set of portfolios. To use an analogy, it is similar to going to a Chinese Buffet. The efficient set is the full menu of dishes in the buffet, while your risk tolerance is akin to the taste buds that make up your palate. A match between the two is your optimal meal at the buffet.
Your low risk selection at the buffet might be something that you have tried many times, say wonton soup. A high risk selection may be a spicy and exotic dish that you never tried before. You might love it ... or hate it. Thus, there's a tradeoff between risk and return.
Incorrect.
Although market participants may act crazy at times resulting in the irrational or nonlinear behavior of asset prices, much of Modern Portfolio Theory assumes that there is a linear relationship between risk and return. The Capital Allocation Line (CAL) and Security Market Line (SML) are two common equations for expressing this relationship.
There are billions of actual or prospective investors in the world. Some investors want a low-risk portfolio. For example, they may put the bulk of their assets in government bonds. Others may want a high-risk portfolio, and put their money in the newest tech IPOs hoping to find the next Google.
In _theory_, how many funds do you need to tailor-make an optimal portfolio for each of these investors?
In the context of Modern Portfolio Theory, there are several special portfolios. The Minimum Variance Portfolio is the risky portfolio with the least amount of risk. The Maximum Variance Portfolio is the risky portfolio with the highest risk. The risk-free asset is the government security, usually a short-term bond, with no risk of loss. The market portfolio is the theoretical portfolio of all risky assets.
Which two assets or funds do you think are needed for the Two Fund Separation Theorem to work properly?
Incorrect.
Although the result may be surprising, fewer than three portfolios are needed, in theory.
Incorrect.
The Maximum Variance Portfolio is generally not part of the efficient frontier in Markowitz Portfolio Theory. Therefore, it is not used in the Two Fund Separation Theorem. Diversification provides you with one of the few “free lunches” in finance, giving the equivalent of higher returns and lower risk up to an extent.
Some investors have a relatively high risk tolerance. The risk of the portfolios may exceed the market as a whole. For example, they may hold a lot of technology stocks in their portfolios. However, there may be other more efficient ways to increase the risk of your portfolio without investing in a bunch of high-flying stocks.
How can you achieve an expected return higher than the market portfolio return if you only have two funds, the risk-free asset and the market portfolio?
Incorrect.
The risk-free asset and Minimum Variance Portfolio are essentially the same thing, if a risk-free asset exists. The risk (for example, standard deviation or beta) in this case is zero. If a risk-free asset does not exist, then the Minimum Variance Portfolio is the leftmost portfolio (or the one with the lowest variance or standard deviation) on the Markowitz efficient frontier.
Incorrect.
It is possible by using leverage, given the reasonable assumption that the expected return on the market portfolio is higher than the rate at which you can borrow.
Correct!
If you have a higher risk tolerance than the market portfolio, your optimal portfolios may be achieved by borrowing capital at the risk-free rate of interest and then reinvesting the proceeds in the market portfolio. This “borrowing portfolio” remains on the Capital Allocation Line (CAL) of optimal risky portfolios. It extends the straight line between the risk-free asset and market portfolio beyond the market portfolio in a linear manner.
The borrowing and lending portfolios are shown in the picture below.
Incorrect.
Although your risk tolerance plays a role in selecting your optimal portfolio, it does not affect the overall risk-return relationship according to Modern Portfolio Theory.
Incorrect.
An optimal portfolio for all investors can be created by having much fewer than an infinite set of portfolios.
Incorrect.
Putting 100% of your assets in the market portfolio gives you a return exactly equal to the market portfolio, not higher.
In summary:
[[summary]]
When it comes to Modern Portfolio Theory, do you think this relationship between risk and expected return can be expressed as a straight line?
Correct!
The straight line relationship comes from something you learned in basic algebra. A line can be drawn between any two points. In our context, the points refer to portfolios. The line represents the trade-off between risk and return. The more risk you are willing to accept, the higher your _expected_ return.
Although market participants may act crazy at times resulting in the irrational or nonlinear behavior of asset prices, much of Modern Portfolio Theory assumes that there is a linear relationship between risk and return. The Capital Allocation Line (CAL) and Security Market Line (SML) are two common equations for expressing this relationship.
Correct!
This result is called the __Two Fund Separation Theorem__. Two funds are all that is needed to construct optimal portfolios for all investors, according to the Theorem. It might be boring to run an investment management firm with only two funds, but theoretically, this is all you would need to construct optimal portfolios for your clients.
Two
Three
An infinite number of portfolios
Maximum Variance Portfolio and Market Portfolio
Risk-free asset and Market Portfolio
Risk-free asset and Minimum Variance Portfolio
It is not possible
By using leverage
By putting 100% of your assets in the Market Portfolio.
Yes
No
It depends on my risk tolerance
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