The suitability of a fund or unit investment trust (UIT) is directly related to the individual securities held in their portfolios. For example, the suitability of a large-cap stock fund is relatively the same as the suitability of a large-cap stock. The primary differences between funds/UITs and the individual securities they hold are diversification and fees.

Funds and UITs provide instant diversification to their investors. It’s not uncommon to find dozens, if not hundreds of individual securities in a large portfolio like a mutual fund. Instead of doing the necessary research to find the best investments in the market, an investor can simply invest in a fund or UIT and have a professional invest on their behalf. This is a big benefit, especially for retail investors without the knowledge, time, or patience to invest.

Of course, investments in funds and UITs are not free of cost. We learned about the expense ratio, sales charges, 12b-1 fees, management fees, and other expenses related to investing in these products. While the benefits tend to outweigh the fees for most investors, the cost of investing should be considered when choosing these investments.

**Dollar cost averaging** is a common investment strategy with investment companies, especially mutual funds. It involves an investor making a fixed dollar, consistent purchase of shares (or units) over time. Dollar cost averaging factors out **market timing risk**, which is the risk of putting money in the market at the wrong time.

If an investor made a $100,000 investment right before the Great Recession of 2008 (for example, in the summer of 2007), it would’ve taken over 4 years to recoup the losses from the market downturn. Investors must be aware of the risk of a market collapse soon after making an investment. The larger the investment made, the bigger the risk.

Instead of making one large $100,000 purchase, what if the investor made a $1,000 weekly investment over the course of 100 weeks (roughly 2 years)? As market prices fell, more shares are purchased with the same amount of money. This is how dollar cost averaging mitigates **market timing risk**. In a fluctuating market, the investor’s average cost per share is less than the average price per share. Let’s demonstrate this with an example. Assume the following purchases of ABC mutual fund occur during a market decline:

Date | Purchase amount | Price per share | Shares purchased |
---|---|---|---|

Jan 1 | $1,000 | $20 | 50 |

Feb 1 | $1,000 | $16 | 62.5 |

Mar 1 | $1,000 | $10 | 100 |

Apr 1 | $1,000 | $8 | 125 |

Overall, the investor purchased $4,000 of ABC mutual fund over a four-month period. During that time period, they purchased 337.5 shares. Now, let’s compare the average cost per share to the average price per share:

**Average cost** = $Shares purchasedAmount invested $

**Average cost** = $337.5$4,000 $

**Average cost** = $11.85

Now, find the average price:

**Average price** = $Number of investmentsCombined market prices at purchase $

**Average price** = $4$20 + $16 + $10 + $8 $

**Average price** = $4$54 $

**Average price** = $13.50

The average cost factors in the prices paid and the shares purchased, while the average price is a simple average of the available prices at investment. In a fluctuating market, the average cost will always be lower because investors purchase * more* shares when the market falls. While a bear market tends to work against investors, those who continue to invest bring down their average cost of investing.

A common way to determine the effectiveness of a fund manager is through the use of **alpha**. When calculated, alpha determines whether a fund is over or underperforming expectations. If a test question provides the expected return of a fund, the calculation is fairly simple:

$Alpha=actual return - expected return$

A question could sound something like this:

An investor determines the expected return of a large-cap stock mutual fund over a year to be +14%. At the end of the year, the actual return was +17%. What is the alpha of the fund?

$Alpha=17% - 14%$

$Alpha=3$

A positive alpha of 3 means the fund is over-performing expectations by 3%. This is a sign the fund manager is doing a good job of managing the portfolio. If the alpha was negative, the fund would be underperforming expectations by the amount of the alpha. If the alpha was zero, the fund would be meeting expectations.

Math-based alpha questions can be more complicated, and typically involve another figure - beta. **Beta** correlates the volatility of an investment or portfolio to the volatility of the market. For example, a large-cap stock fund would most likely use the S&P 500 as its benchmark index. If the fund’s volatility was equal to the volatility of the S&P 500, its beta would be 1. If its volatility was twice that of the S&P 500, its beta would be 2. If its volatility was 3 times the S&P 500, but its performance was inverse of the index, its beta would be -3. For an in-depth look at beta, please visit this future chapter and search for the section on beta (disregard the options part of that chapter for now).

There are two types of math-based questions involving both alpha and beta to be aware of. First, let’s explore this question:

An investor is comparing two different funds in an investment analysis. BCD stock fund maintains a beta of 1.0, while TUV stock fund maintains a beta of 1.5. Last year, BCD stock fund’s performance was +14%, while TUV stock fund’s performance was +19%. What is TUV stock fund’s alpha last year?

Given alpha is a measurement of over or underperformance, we must compare the performance of TUV stock (+19%) to its expected performance. The expected performance is not explicitly provided, but we can make an assumption based on the information provided on BCD stock fund. The only reason it’s included in the question is to tell you the performance of the market in a sneaky way. Remember, a beta of 1 means the investment’s volatility is equal to the market. We can safely assume the market (assumptively the S&P 500) performed equally to BCD stock fund, therefore the market return last year was +14%.

TUV stock fund maintains a beta of 1.5, meaning it historically has moved 1.5 times faster than the market. Because beta is positive, we can assume it’s moving in the same direction as the market. With that information, we can take the beta (1.5) and multiply it times the assumptive market return (14%). This tells us the expected return of TUV stock is 21% (1.5 x 14%).

Now, we can use the original alpha formula:

$Alpha=actual return - expected return$

$Alpha=19% - 21%$

$Alpha=-2$

An alpha of -2 means TUV stock fund underperformed expectations by 2%. The fund manager hopefully will do a better job the following year!

There’s another formula you can utilize to calculate alpha involving a few new components. Here it is:

$Alpha=(PR - RF) - (Beta x (MR - RF))$

$Where:PRRFMR =portfolio return=risk-free return=market return $

The portfolio return and market return should be self-explanatory. The risk-free rate of return measures the return on a relatively risk-free security. The most commonly cited risk-free security is the 3 month Treasury bill. It’s very close to being completely free of risk due to its short-term nature and US government backing, although all securities come with at least some risk potential.

Here’s an example of a question involving this formula:

An investor is analyzing the market and the returns of a small-cap stock fund held in their portfolio. The fund was up 28% while maintaining a beta of 2.5 last year. During the same year, the S&P 500 was up 10%, the Russell 2000 was up 14%, and the 3-month Treasury bill gained 2%. What is the small-cap stock fund’s alpha?

This is a tough question, but can you figure it out using the formula above?

(spoiler)

Answer: **-4**

$Alpha=(PR - RF) - (Beta x (MR - RF))$

$Alpha=(28% - 2%) - (2.5 x (14% - 2%))$

$Alpha=26% - (2.5 x 12%)$

$Alpha=26% - 30%$

$Alpha=-4$

This fund manager underperformed expectations by 4%, leading to an alpha of -4.

One note to point out in the question - both the S&P 500 and the Russell 2000 returns were provided, but only the Russell 2000 was utilized. Given the fund is a small cap stock fund, it’s important to utilize the index that is most correlated with the fund. The S&P 500 contains large and mid-cap stocks, while the Russell 2000 is a small-cap stock index. Therefore, the S&P 500 should be disregarded.

Alpha is most relevant in determining the effectiveness of an actively managed fund because these fund types aim to outperform their benchmarks (their relevant market index). If a small-cap stock fund manager seeks to pick the top small-cap stocks in the Russell 2000, alpha serves as a good measure of their successes or failures. If the stocks they choose outpace the index on average, they’ll attain a positive alpha. The higher the alpha, the better their investments are performing. And vice versa.

Passively managed funds are built to match the performance of their benchmarks, and therefore should maintain alpha values near zero (meaning they don’t over or underperform the market). The same concept applies to beta as well; passively managed funds should maintain a beta near 1 (meaning they move at the same volatility as the market).

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