Investors want to earn the highest return possible for a level of risk that they are willing to take. So how does an investor allocate her capital to maximize her investment utility — the risk-return profile that yields the greatest satisfaction? The simplest way to examine this is to consider a portfolio consisting of 2 assets: a risk-free asset that has a low rate of return but no risk, and a risky asset that has a higher expected return for a higher risk. Investment risk is measured by the standard deviation of investment returns— the greater the standard deviation, the greater the risk. By varying the relative proportions of the 2 assets, an investor can earn a risk-free return by investing all her money in the risk-free asset, or she can potentially earn the maximum return by investing entirely in the risky asset, or she can select a risk-return trade-off that is anywhere between these 2 extremes by selecting varying proportions of the 2 assets.
Capital Allocation Line (CAL)
Asset allocation is the apportionment of funds among different types of assets, such as stocks and bonds, having different ranges of expected returns and risk. Capital allocation, on the other hand, is the apportionment of funds between risk-free investments, such as T-bills, and risky assets, such as stocks. The simplest case of capital allocation is the allocation of funds between a risky asset and a risk-free asset. The risk-return profile of this 2-asset portfolio is determined by the proportion of the risky asset to the risk-free asset. If this portfolio consists of a risky asset with a proportion of y, then the proportion of the risk-free asset must be 1 − y.
One way to adjust the riskiness of a portfolio is by varying the proportion of the risk-free asset and the risky asset. The investment opportunity set is the set of all combinations of the risky and risk-free assets, which graphs as a line when plotted as return against risk, as measured by the standard deviation. The line begins at the intercept with the minimum return and no risk of the risk-free asset, when the entire portfolio is invested in the risk-free asset, to the maximum return and risk when the entire portfolio is invested in the risky asset. Hence, this capital allocation line (CAL) is the graph of all possible combinations of the risk-free asset and the risky asset.
The slope of the capital allocation line = the incremental return of the portfolio to the incremental increase in risk. Hence, the slope of the capital allocation line is called the reward-to-variability ratio because the expected return increases continually with the increase in risk as measured by the standard deviation.
Slope of CAL
=
Reward-to-Variability Ratio
=
Portfolio Return − Risk-Free Return Standard Deviation of Portfolio
The risk-free return is subtracted from the portfolio return to yield the proportion of the return due to the risky asset. The increased return for the increased risk is the reward for accepting the increased risk — the risk premium.
Capital Market Line (CML)
The capital market line (CML) is the capital allocation line formed when the risky asset is a market return rather than a single-asset return.
No investment is totally risk-free, but United States Treasuries come close. Although T-bills are often cited as being closest to the ideal risk-free asset for their short terms and low interest rate risk, they do have reinvestment risk. Another security that is close to the ideal are Treasury-Inflation Protected Securities (TIPS), which pay a fixed interest rate on a principal that is adjusted for inflation. For their term length, which can be 5, 10, or 20 years, there is no reinvestment risk, and the interest rate risk is mitigated by the increasing principal, since some of the change in prevailing interest rates results from changes in inflation.
For the risky asset, many investors choose a mutual fund or an exchange-traded fund based on a market index, which provides some diversification in the risky asset without the need for security analysis. This passive strategy of selecting a market index security or investment for the risky asset is sometimes called the mutual fund theorem.
Capital allocation is the allotment of funds between risk-free assets, such as Treasury bonds, and risky assets, such as equities. The CAL is represented as a line graph. The y-axis is the expected return, and the x-axis is the amount of risk, usually measured by the standard deviation of returns.
Capital allocation line (CAL) is a graph created by investors to measure the risk of risky and risk-free assets. The graph displays the return to be made by taking on a certain level of risk. Its slope is known as the "reward-to-variability ratio". An example capital allocation line.
The capital allocation line (CAL) makes up the allotment of risk-free assets and risky portfolios for an investor. CML is a special case of the CAL where the risk portfolio is the market portfolio. Thus, the slope of the CML is the Sharpe ratio of the market portfolio.
It is given by the subtraction of expected return on risky assets and rate of return on risk-free assets, all divided by the standard deviation of a portfolio of risky assets. An approach investors might take to manipulate a portfolio's risk level is to modify the amount allocated to risk-free assets.
Capital Allocation to Risky Assets is making the choice of how much to invest in the risky portfolio relative to the risk-free portfolio. An investor's own risk tolerance informs this choice. The return on T-bills technically has a standard deviation.
Answer and Explanation: The combination of the two assets specified will result in a risk-adjusted portfolio with a moderate level of risk. The actual level of risk of the entire portfolio will be based on the percentage of the portfolio each asset represents.
Companies use many different methods to allocate their capital. These include return on investment (ROI), net present value (NPV), and payback period. Capital allocation is a critical part of a company's management. It can have a major impact on the company's profitability and growth.
A steeper line means that the investor gets more return per extra unit of risk taken. The capital allocation line is steepest when it is tangential to the efficient frontier, and it is here we get the optimal risky portfolio.
What is the efficient frontier with 2 risky assets and 1 risk-free assets? It is a straight line through the risk-free rate and the portfolio of assets 1 and 2 that has the highest Sharpe ratio.
The CML cells grow and survive better than normal cells. CML doesn't completely interfere with the development of mature red cells, white cells and platelets. Therefore, chronic phase CML is generally less severe than acute leukemia.
Tests Used To Diagnose CML. Complete Blood Count (CBC) with Differential. This test is used to measure the number red blood cells, white blood cells and platelets in a sample of blood. It also measures the amount of hemoglobin in the red blood cells and the percentage of red blood cells in the sample.
The introduction of a risk-free asset changes the efficient frontier into a straight line. This straight efficient frontier line is called the Capital Market Line (CML) for all investors, and Capital Allocation Line (CAL) for one investor.
Clearly the best portfolio to hold in combination with the riskfree rate is the tangency portfolio because it has the highest slope. Any other portfolio would be inefficient. The line between the riskfree rate and the tangency portfolio is called the capital allocation line.
The CML is the Capital Market Line which is a visual representation of the relationship between expected return and risk.The CAL is the Capital Asset Pricing Line. This is an extension of the CML and it shows the trade-off between risk and return for a well-diversified portfolio.
The line E(Rc) = Rf + Spσ(Rc) is the capital allocation line (CAL). The slope of the line, Sp, is called the Sharpe ratio, or reward-to-risk ratio. The Sharpe ratio measures the increase in expected return per unit of additional standard deviation.
Risk-free return is the theoretical return attributed to an investment that provides a guaranteed return with zero risk. The risk-free rate represents the interest on an investor's money that would be expected from a risk-free asset when invested over a specified period of time.
Introduction: My name is Gregorio Kreiger, I am a tender, brainy, enthusiastic, combative, agreeable, gentle, gentle person who loves writing and wants to share my knowledge and understanding with you.
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