Over the past few weeks we have discussed some of the key building blocks for the construction of a portfolio.
We identified standard deviation as a measure of risk or volatility. The higher the standard deviation of a security (or a portfolio of securities), the greater the risk.
We came up with several methods to measure risk. We can use the simple mean (or average), the time-weighted return (also known as geometric return), and the money-weighted return. When evaluating investment or fund managers, we use the time-weighted return, because it allows us to most appropriately evaluate performance in light of flows into and out of a portfolio or fund over an extended period of time during which performance may vary.
Last week I introduced Beta which is the measure of the risk of a security (or a portfolio of securities) in comparison to the market overall. We learned a common proxy for the market is the Standard & Poor’s 500 index. The convention in portfolio theory is that the market has a beta of 1. A security with a beta greater than 1 will have price movements that are greater than the market. A security with a beta less than the market will have price movements that are less than the market.
We’re still missing a critical piece of information. That is the way in which securities (or asset classes) perform in relation to each other. This is called “correlation.” We’re looking for securities that will provide diversification. If some of the securities in the portfolio are “zigging,” we want others to be “zagging.”
We can calculate this relationship between securities with correlation coefficient. The formula is a bit involved. So, I won’t post it here.
Correlation is measured from -1 to +1. Securities that have a correlation of -1 are perfectly negatively correlated. If one moves up by 10%, the other will move down by exactly 10%. Securities that have a correlation of +1 are perfectly positively correlated. If one moves up by 10%, the other moves up by exactly 10%. Securities that have a correlation of 0 have no relationship with each other.
In reality most securities are positively correlated with each other. Intelligent Investors are interested in building a portfolio that will be well-allocated across asset classes. The less correlated the asset classes in the portfolio the lower the risk. You can Google “asset class correlation” and find all kinds of data on asset class correlation.
I’ll have more to say about correlation in future posts.
Wednesday, November 24, 2010
Friday, November 19, 2010
Beta
Back to the classroom. In the past two weeks I have written about how to measure risk and return. We learned that we use standard deviation to measure the risk of a security. There are several methods to measure return, including the simple mean, the time-weighted return (also known as geometric return), and the money-weighted return.
So, now the question is, how do we combine securities in a portfolio? Can we simply add securities until we reach some reasonable number? Maybe 30 or 40?
Actually, what we really need to know is how securities act in the marketplace. How do they perform relative the market itself? We might consider the Standard & Poor’s 500 index as a proxy for the market.
We can readily find data for the return of the S&P 500 index. What about the risk of the market? The Capital Asset Pricing Model describes risk with the term Beta. Beta is a measure of volatility of a security. The market itself is assigned a beta of 1. The beta for any security can be calculated through regression analysis. Beta tells us how much the price of a given security will move relative to the market.
If a security has a beta of 1.0, its price movements will mirror the market. A security with a beta greater than 1.0 will be more volatile or risky than the market. A security with a beta less than 1.0 will be less risky than the market. If a security has a beta of 1.5, it will be 50% more risky than the market. A security with a bet of 0.75 will be 25% less risky than the market. What about a beta of zero? This means that there is no statistical relationship between the security and the market. A negative beta indicates that the security acts in opposition to the market. If the market return were up 10%, a security with a beta of -1.0 would theoretically be down by 10%.
So, does that give us enough information to start building our portfolio? No. Come back next week for another critical piece of this puzzle.
So, now the question is, how do we combine securities in a portfolio? Can we simply add securities until we reach some reasonable number? Maybe 30 or 40?
Actually, what we really need to know is how securities act in the marketplace. How do they perform relative the market itself? We might consider the Standard & Poor’s 500 index as a proxy for the market.
We can readily find data for the return of the S&P 500 index. What about the risk of the market? The Capital Asset Pricing Model describes risk with the term Beta. Beta is a measure of volatility of a security. The market itself is assigned a beta of 1. The beta for any security can be calculated through regression analysis. Beta tells us how much the price of a given security will move relative to the market.
If a security has a beta of 1.0, its price movements will mirror the market. A security with a beta greater than 1.0 will be more volatile or risky than the market. A security with a beta less than 1.0 will be less risky than the market. If a security has a beta of 1.5, it will be 50% more risky than the market. A security with a bet of 0.75 will be 25% less risky than the market. What about a beta of zero? This means that there is no statistical relationship between the security and the market. A negative beta indicates that the security acts in opposition to the market. If the market return were up 10%, a security with a beta of -1.0 would theoretically be down by 10%.
So, does that give us enough information to start building our portfolio? No. Come back next week for another critical piece of this puzzle.
Wednesday, November 10, 2010
Measuring Return
Let’s continue our discussion of Modern Portfolio Theory. Last week I suggested that portfolio construction involves carefully selecting securities based on their risk and return characteristics.
I probably should have mentioned that return can be calculated in various ways. The simplest is the mean or average. To calculate this return we simply add up all the returns and divide by the total numbers of return in the data set. If we had annual returns from 2000-2004 of -9.1%, -11.9%, -22.1%, 28.7% and 10.9%, the average return would be -0.70%. This was the actual return of the Standard & Poor’s 500 index.
When evaluating investment advisors, fund managers or portfolio managers, there is a different measure that gives us better insight into performance. Time-weighted return eliminates the distortions caused by the inflows and outflows of money over time. This is also called the geometric mean. It is calculated using holding period returns (HPR) for each investment period (e.g. a year) and linking them together.
The formula for holding period return is (ending value - beginning value + dividends/interest +/- other cash flow) divided by the beginning value.
To calculate time-weighted returns we add 1 to each of these HPRs, multiply these values against each other then subtract 1 from that result.
Here’s the formula
= [(1 + HPR1)*(1 + HPR2)*(1 + HPR3) ... *(1 + HPRN)] - 1.
If the investment period is greater than 1 year, then we need to annualize the return for the HPRs we calculated. The formula for this is (1 + compounded rate)1/Y – 1 where Y is the total time of years.
Yet another way to measure performance is money-weighted return. This involves calculating the internal rate of return. We calculate the return that will cause the inflows and outflows to be equal. For investment outflows include the purchase price, reinvested dividends or interest and contributions. Inflows include the proceeds from the sale of the investment, dividends or interest received and withdrawals. Calculating money-weighted return requires using Microsoft Excel or a financial calculator. We use the money weighted return instead of holding period return for investment periods that are greater than 1 year.
Source for formulas: Investopedia
I probably should have mentioned that return can be calculated in various ways. The simplest is the mean or average. To calculate this return we simply add up all the returns and divide by the total numbers of return in the data set. If we had annual returns from 2000-2004 of -9.1%, -11.9%, -22.1%, 28.7% and 10.9%, the average return would be -0.70%. This was the actual return of the Standard & Poor’s 500 index.
When evaluating investment advisors, fund managers or portfolio managers, there is a different measure that gives us better insight into performance. Time-weighted return eliminates the distortions caused by the inflows and outflows of money over time. This is also called the geometric mean. It is calculated using holding period returns (HPR) for each investment period (e.g. a year) and linking them together.
The formula for holding period return is (ending value - beginning value + dividends/interest +/- other cash flow) divided by the beginning value.
To calculate time-weighted returns we add 1 to each of these HPRs, multiply these values against each other then subtract 1 from that result.
Here’s the formula
= [(1 + HPR1)*(1 + HPR2)*(1 + HPR3) ... *(1 + HPRN)] - 1.
If the investment period is greater than 1 year, then we need to annualize the return for the HPRs we calculated. The formula for this is (1 + compounded rate)1/Y – 1 where Y is the total time of years.
Yet another way to measure performance is money-weighted return. This involves calculating the internal rate of return. We calculate the return that will cause the inflows and outflows to be equal. For investment outflows include the purchase price, reinvested dividends or interest and contributions. Inflows include the proceeds from the sale of the investment, dividends or interest received and withdrawals. Calculating money-weighted return requires using Microsoft Excel or a financial calculator. We use the money weighted return instead of holding period return for investment periods that are greater than 1 year.
Source for formulas: Investopedia
Wednesday, November 3, 2010
Standard Deviation
I will be teaching the Investment course in the CFP certificate program at the University of Portland over the next several weeks. The course provides an overview of investing fundamentals. I encourage students to think of the class as a fast paced review of many concepts. We run through them quickly and rarely go very deep into any subject.
One area that merits a bit more attention is Modern Portfolio Theory. Most investment advisors rely on MPT to build and manage portfolios. The theory involves attempting to manage the relationship between risk and return in a basket of securities. Using various research sources (e.g. Morningstar) we can identify the risk and return characteristics of a given security. MPT tells us we should combine securities in a way that maximizes the risk adjusted return of the portfolio.
How do we measure risk? First, we need to define risk. This is the chance that the return from the security will not be what we expected. We are, of course, concerned with returns that fall below our expectation. We’re happy if returns exceed our expectations.
We can measure risk using Standard Deviation. This measures the dispersion of historical returns from its mean (i.e. average). We take the square root of the variance to calculate standard deviation.
If a security earned 8% year after year, there would be no dispersion and, therefore, no risk. The mean would be 8% and the standard deviation would be 0.
But if the security earned -12% one year, +16% the next and +20% the following year, the mean would still be 8%. But the dispersion (and the risk) would be much greater. In fact, the standard deviation for that security is 17. Which would you rather own?
Intelligent Investors understand MPT and they use it wisely to build and manage their portfolios. I will be discussing other concepts that underlie MPT in future posts.
One area that merits a bit more attention is Modern Portfolio Theory. Most investment advisors rely on MPT to build and manage portfolios. The theory involves attempting to manage the relationship between risk and return in a basket of securities. Using various research sources (e.g. Morningstar) we can identify the risk and return characteristics of a given security. MPT tells us we should combine securities in a way that maximizes the risk adjusted return of the portfolio.
How do we measure risk? First, we need to define risk. This is the chance that the return from the security will not be what we expected. We are, of course, concerned with returns that fall below our expectation. We’re happy if returns exceed our expectations.
We can measure risk using Standard Deviation. This measures the dispersion of historical returns from its mean (i.e. average). We take the square root of the variance to calculate standard deviation.
If a security earned 8% year after year, there would be no dispersion and, therefore, no risk. The mean would be 8% and the standard deviation would be 0.
But if the security earned -12% one year, +16% the next and +20% the following year, the mean would still be 8%. But the dispersion (and the risk) would be much greater. In fact, the standard deviation for that security is 17. Which would you rather own?
Intelligent Investors understand MPT and they use it wisely to build and manage their portfolios. I will be discussing other concepts that underlie MPT in future posts.
Subscribe to:
Posts (Atom)
