18 Questions
Which asset is considered 'dominated'?
Asset D
What type of investor would prefer Asset C according to the text?
Risk-neutral investor
Which asset would be best suited for an investor not overly risk-averse and not quite risk-neutral according to the text?
Asset B
What aspect should an investor consider when choosing among undominated assets?
Degree of personal willingness to trade-off return for less risk
In portfolio optimization, which combination does the text suggest by allowing investment in cash (asset A) and another asset?
Combination of A and C
What is the primary reason for preferring assets closer to X and further away from Y as mentioned in the text?
Higher return and lower risk
How does holding both assets in a portfolio affect the standard deviation compared to holding them individually?
The standard deviation is lower
In a perfectly negatively correlated scenario (R = -1), what happens to the means and standard deviations of the combined assets B and C?
Means increase but standard deviations decrease
How is risk affected when investing in a portfolio of risky assets B and C if they are imperfectly correlated?
Risk decreases with correlation
What happens to the risk level at point Z on the graph in Figure 5 when judiciously choosing the fraction of money invested in asset B?
Risk decreases to zero
How does diversification impact expected return in a portfolio?
It has no effect on expected return
What mathematical formula represents the standard deviation of a portfolio combining assets B and C, considering their correlation and fractions invested?
$S_P = (fS_B + (1 − f)S_C)^2 - 2f(1 − f)(1 − R)S_BS_C$
What is the primary focus of portfolio theory?
Diversification to reduce portfolio risk
In the context of portfolio theory, what does the mean represent?
The return one expects to obtain on average
How does standard deviation relate to total return in portfolio theory?
It measures the dispersion of total return
What did Harry Markowitz formalize in 1952 that became a cornerstone of modern financial theory?
The benefits of diversification in investment portfolios
For a bell-shaped distribution of total return, how often would one expect the actual return to fall within two standard deviations of the mean?
95% of the time
What role does diversification play in an investment portfolio according to portfolio theory?
It reduces the risk of the portfolio
Study Notes
Portfolio Theory
- Portfolio theory is concerned with the risk-reducing role played by individual assets in an investment portfolio of several assets.
- Harry Markowitz formalized the benefits of diversification in 1952 and was awarded the Nobel Prize in economics for this work.
Means and Standard Deviations of Total Return
- The return and risk of an asset are commonly measured in terms of the mean and standard deviation of total return.
- Total return represents income plus capital gains or losses.
- The mean is the return one expects to obtain on average.
- Standard deviation is a measure of dispersion, in this case total volatility of return.
Properties of Standard Deviation
- For bell-shaped distributions, the return one actually experiences will fall within:
- One standard deviation to either side of the mean about 68% of the time.
- Two standard deviations about 95% of the time.
- Three standard deviations about 99.7% of the time.
Diversification
- Holding both assets in a portfolio leads to a reduction in risk without sacrificing expected return.
- Diversification can be illustrated graphically, showing the combination of assets B and C.
- When B and C are perfectly negatively correlated (R = -1), the portfolio can have zero risk by choosing the right fraction of money invested in B.
Undominated Assets
- Assets are said to be dominated if they have lower expected returns and higher standard deviations than others.
- In a graph of expected returns vs. standard deviations, dominated assets can be easily ruled out.
- The choice among undominated assets depends on the investor's risk tolerance.
Portfolios of a Riskless and a Risky Asset
- A portfolio of a riskless asset (e.g., cash) and a risky asset can reduce risk without sacrificing expected return.
- The optimal choice of assets depends on the investor's risk tolerance.
Learn about the benefits of holding a diversified portfolio in finance. Understand how combining assets can lead to lower risk without sacrificing expected return. Explore the concept graphically and discover the impact of correlation on portfolio outcomes.
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