Capital market line is the graph of the required return and risk (as measured by standard deviation) of a portfolio of a risk-free asset and a basket of risky assets that offers the best risk-return trade-off. It is a special case of capital allocation line that is tangent to the efficient frontier and the slope of the capital allocation line represents the Sharpe ratio.
Icare unlimited for mac. You might want to review the article on risk and return to obtain an understanding of the portfolio expected return, portfolio standard deviation and their interplay using the efficient frontier.
A well-diversified portfolio of risky assets has zero unsystematic risk. The point on efficient frontier that has the lowest risk is called the global minimum variance portfolio. If an investor has an option to borrow and lend at the risk-free rate, he can create an asset allocation which is a mix of the risk-free asset and the portfolio of risky portfolio.
The efficient frontier is the set of portfolios that gets us the highest expected return for any given risk level. Or from another perspective, the minimum amount of risk for an expected return. To trace this line, we can define a variable frontiery. Going back to the chart above, we can see the maximum return doesn’t go much higher than 0.3. Apr 17, 2018 The Efficient Frontier. https://bestnfile570.weebly.com/free-spiderman-friend-or-foe-iso-pc-download.html. A portfolio frontier is a graph that maps out all possible portfolios with different asset weight combinations, with levels of portfolio standard deviation graphed on the x-axis and portfolio expected return on the y-axis.
Risk-free asset is an asset that has zero risk i.e. zero standard deviation. US treasury securities can be considered risk-free assets for this analysis.
Expected return of a portfolio of a risk-free asset and a portfolio of risky asset can be determined using the following formula:
$$ text{E}(text{R})=text{w} _ text{r}times text{r} _ text{f}+(text{1}-text{w} _ text{r})times text{r} _ text{p} $$
Where wr is the weight of the risk-free asset, rf is the risk-free rate of return and rp is the return on the portfolio of risky assets.
Standard deviation of a portfolio of risk-free asset and risky assets can be expressed using the following equation:
Graphing Efficient Frontier In Excel
$$ sigma=sqrt{text{w}^text{2}{sigma _ text{r}}^text{2}+{(text{1}-text{w})}^text{2}{sigma _ text{p}}^text{2}+text{2w}(text{1}-text{w})sigma _ text{r}sigma _ text{p}rho} $$
Graphing Efficient Frontier In Excel
Where w is weight of the risk-free asset, σr is standard deviation of risk-free asset, σp is the standard deviation of the portfolio of risky assets and ρ is the correlation coefficient of returns of risk-free asset and the portfolio of risky assets.
Because a risk-free asset has zero standard deviation and its correlation with a portfolio of risky asset is zero, the above equation can be simplified as follows:
$$ sigma=sqrt{{(text{1}-text{w})}^text{2}{sigma _ text{p}}^text{2}} $$
After some mathematical manipulation we can arrive at the following equation which represents the capital allocation line:
$$ text{E}(text{R})=text{r} _ text{f}+frac{text{E}(text{R})-text{r} _ text{f}}{sigma _ text{P}}timessigma $$
Where E(R) is the expected return on the portfolio of the risk-free asset and risky assets, rf is the risk-free rate, σP Garuda puranam telugu book pdf. is the standard deviation of the portfolio of risky assets and σ is the standard deviation of the new portfolio (comprising of both the risk-free rate and the risky assets). The factor of (E(R) – rf)/σP) measures the return in addition to the risk-free rate per unit of risk. It is also called rewards-to-risk ratio. It is the slope of the capital allocation line.
Example
In the example of efficient frontier, we identified a set of portfolios that offer same risk-return trade-off. Let’s combine risk-free asset with expected return of 3% with the portfolio B and D.
The following table shows the expected return and standard deviation of Portfolio B and D:
Portfolio | Portfolio Standard Deviation | Portfolio Expected Return |
---|---|---|
B | 4.87% | 11.20% |
D | 3.39% | 9.60% |
The following shows the expected return and standard deviation of a mix of risk-free asset and portfolios B and D:
Weight of Risk-Free Asset | E(R) of Rf and Portfolio B | σ of rf and Portfolio B | E(R) of Rf and Portfolio D | σ of rf and Portfolio D |
---|---|---|---|---|
100% | 3.00% | 0.00% | 3.00% | 0.00% |
80% | 4.64% | 0.97% | 4.32% | 0.68% |
60% | 6.28% | 1.95% | 5.64% | 1.36% |
40% | 7.92% | 2.92% | 6.96% | 2.03% |
20% | 9.56% | 3.89% | 8.28% | 2.71% |
0% | 11.20% | 4.87% | 9.60% | 3.39% |
Let’s plot these values on top of the efficient frontier graph:
Capital Allocation Line vs Capital Market Line
The captial allocation line is a graph that represents the risk and return profile of a portfolio that is a combination of the risk-free rate and ANY portfolion on the efficient frontier. Both the lines in the above graphs (representing the combination of risk-free asset and Portfolio C and risk-free asset and Portfolio D) are capital allocation lines.
The capital allocation line representing the mix of risk-free asset and Portfolio D (let’s call it CAL 1) is superior to the capital allocation line of risk-free asset and Portfolio B (let’s call it CAL 2). It is called the capital market line and it is the best possible way in which the risk-free rate and a portfolio of risky assets can be mixed. This is because at all risk levels i.e. standard deviation levels, CAL 1 offers a higher return. The portfolio at the intersection of the efficient frontier and the capital allocation line is the optimal portfolio.
Capital market line is a pre-cursor to the security market line.
by Obaidullah Jan, ACA, CFA and last modified on
Studying for CFA® Program? Access notes and question bank for CFA® Level 1 authored by me at AlphaBetaPrep.com
Studying for CFA® Program? Access notes and question bank for CFA® Level 1 authored by me at AlphaBetaPrep.com
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The concept of Efficient Frontier was first introduced by Harry Markowitz in his paper on Portfolio Selection (1952 Journal of Finance).
The portfolio theory considers a universe of risky investments and explores these possible investments in order to find the optimum portfolio. So, for a given amount of risk, MTP explains how select a portfolio with maximum returns, and with a given amount of return, MTP explains how to select a portfolio with minimum risk.
Suppose you have all the required data (expected returns, volatility, and correlations) for all the investments you are considering. Using this data, you can create various portfolios with different portfolio risk and return profiles.
Among all these portfolios, choose the optimal portfolios in either of the following way:
- Identify all the portfolios that have the same risk (volatility). From this sub-set of portfolios, choose the one that has the highest return.
- Identify all the portfolios that have the same returns. From this sub-set of portfolios, choose the one that has the lowest risk.
Both the methods will product a set of optimal portfolios. This set of optimal portfolios is called the efficient frontier. (Later in this post, we will learn how to construct an efficient frontier in Excel)
If you plot all the portfolios that you could make using the universe of risky securities that you have, the graph will look something like the one below:
Warcraft 3 reign of chaos torrent iso ps2. Each red dot represents the mean and standard deviation of a portfolio. The blue line is the efficient frontier. The efficient frontier has all the optimal portfolios we selected above. Portfolios on the efficient frontier have maximum return for a given level of risk or, alternatively, minimum risk for a given level of return. Clearly, a rational investor will select a portfolio on the efficient frontier.
Dominated Portfolio
In the above graph, you see that for the same level of risk there are multiple portfolios providing different levels of return. A portfolio is said to be dominated, if there is atleast one portfolio that has higher return and lower standard deviation. In other words, a portfolio is dominated if there is any other portfolio to its north-west. So, in the above graph, all portfolios other than those on the efficient frontier are dominated.
Typically, the portfolios that make the efficient frontier are the most diversified ones. Less diversified portfolios tend to be closer to the middle of the achievable region.
Constructing an Efficient Frontier in Excel
The attached PDF file shows you how you can construct an efficient frontier using excel.