Investor X has very high risk tolerance and seeks high returns. Assume capital markets are in equilibrium. Given his low risk aversion and his return objective, and based on capital market theory, Investor X should most appropriately hold:
a) a high-beta portfolio of risky assets financed in part by borrowing at the risk-free rate.
b) a high risk stock, as it will have high expected returns in equilibrium.
c) the market portfolio as his only risky asset.
Considering his low risk aversion , high risk tolerance and his high return objectives I would incline towards answer A. As I understand the investor would select a very risky portofolio for the extra return he gets by borrowing at the risk free rate .
Note that for all investors the market portfolio is equal (separation theorem) and is theoretically composed of all risky assests in existence.
If the investor has an absolutely high risk-aversion he will hold a portfolio of 100% the risk-free asset. If the investor as a very low risk risk aversion (as above) he will have only the market portfolio. (His indifferece curve is relatively flat and will be tangent to the capital market line at a higher point.) There may be even cases where the risk aversion is so low that the investor is 100% invested in the market portfolio and on top uses leverage to further enhance his return.
Best thing here is to visualize the CAPM on a sheet and then play around with different indifference curves to see what happens.
What is then the difference / or how can I measure the difference between a low risk averse Investor who will have only the market portfolio and a very low risk averse investor that uses leverage to borrow at the risk free rate and invest in market portofolio in the question ? It sounds the same to me.
Can it be the High Beta portofolio the reason answer A is wrong? Is a High beta portofolio on the CML- or on the CML the beta is 1?
If I get it right, for this question you don’t need to measure or judge the degree of risk aversion of the investor.
As Oscar perfectly explained, you have only 3 options: holding only risk-free assets, holding only the market portfolio or holding a mixture of both (that option also comprises borrowing at the risk-free rate to invest more than 100% in the market portfolio).
The investor has a high risk tolerance, so we know he’s not going to invest 100% in risk-free assets. From there, we are certain that the will hold the market portfolio.
Under the CAPM model, the market portfolio is the ONLY optimal portfolio in which to invest, given the risk-free rate (it has the best trade-off between risk and return). Consequently, investors only hold a portfolio that lies on the SML. Investing in other portfolios is not optimal (whatever the Beta) - the two first answers are just here to make it confusing.
He will. For example, a risk-averse investor may hold 80% in risk-free assets and 20% in the market portfolio.
An investor with more risk tolerance could invest 30% in risk-free assets, and 70% in the market portfolio.
And someone even less risk averse could borrow 50% of its portfolio at the risk-free rate, and invest 150% in the market portfolio (on a graph, the portfolio would lie on the right hand side of the market portfolio).
In the 3 scenarios, investors choose to hold a portfolio on the security market line. The only risky portfolio in which they invest is the market portfolio (that contains in theory all risky assets).
I don’t think being low risk averse violates any assumption.
Investors are all risk averse, but the degree of risk aversion is variable and depends on the investor. Some are low risk averse, while other are high risk averse.
And I think I figured it out right now (A) would be correct if: Investor would hold a high beta MARKET portfolio (not just any portfolio)"financed by borrowing at the risk free rate
No, the Beta of the market portfolio is always equal to 1 (since Beta is calculated as the covariance of the market with the portfolio, divided by the market portfolio variance).
There is no such thing as a high-beta market portfolio.
The market portfolio is unique (given a level of risk-free rate), and is a combination of ALL risky assets (even though the individual assets’ weights differ).
This is correct. According to the CAPM every individual will have a different grade of risk-aversion, i.e. will have a different risk-return indifference curve. The less risk-averse an individual is the more flatter his indifference curve will be and the higher the tangent point on the CML.
I really encourage you to draw the CAPM model on a sheet of paper and then play around with different indifference curves (steeper curves for high risk-aversion and flatter curves for low risk-aversion). You will immediately see that the different tangent points with the CML will determine the mix of market portfolio and risk-free asset. Regards,