The high discounts are probably due to the funds (at least HQH) not paying dividends on capital gains, as they used to until recently. This change of policy may have upset some holders that chose to sell, but for me it offers a tax advantage. Moreover, those sales by dividend-seeking investors may not have found enough buyers yet, because institutional investors don’t pay much attention to CEFs, given their limited liquidity and their expenses (institutions can buy the underlying assets directly, at reasonable cost).

Therefore, it seems life-sciences as a whole, and HQH in particular, need buyers. I’m trying to help.

The recent debate on the passing of the new health bill may be putting some doubts (i.e., risk) on the healthcare business, but the effect on pharmaceuticals and diagnosis equipment, if any, would most probably be positive. I mean, I don’t see grounds for claiming that those reforms may be lessening the attractiveness of these companies.

The expense ratios are around 1,5%. It doesn’t look expensive,  given the 20% discount, for funds are actively managed and reasonably diversified. Their portfolios contain pharmaceuticals mostly, with an interesting allocation in diagnosis and medical devices, among other subsectors.

Qualitatively, I think the sector is a good bet for the long run, as humanity will probably spend more and more on health, and the US has a comparative advantage in that business. Despite their differing names, both funds have similar portfolios, so I preferred HQH because its discount was higher.

The bottom line is that I don’t see a 20% discount to be justified, and I am comfortable with holding a piece of the US life-sciences business in my portfolio. HQH looks like an interesting asset for the long term, but I think it would be smart to re-assess if the discount shrinks.

Disclaimer: This is just an opinion, not a recommendation to buy. I am long on HQH. This and other trades are shown on my covestor profile.

1. Mutual funds, also called open-end companies.
2. Closed-end companies, also called closed-end funds.
3. Unit investment trusts.

Therefore, the correct term is closed-end fund, without the mutual. Closed-ended fund is also acceptable.

Sometimes close-ended fund is used, even close-end fund. I wasn’t sure about the validity of those ones, so I googled a few authoritative investment sites, that have no user-generated content, to see how frequently  (according to Google) each variation is used:

The table shows the instances for each of the indicated terms, followed by fund or funds (I added together both alternatives). The sole appearance of close-ended fund(s) is due to what an investment company filled-in in a form, so I wouldn’t take that as coming from an utmost authority.

My conclusion is that closed-end fund(s) is the preferred term, while closed-ended fund(s) is also acceptable.

By the way, exchange-traded funds (ETFs) are either mutual funds or unit investment trusts.

If we ask for the average grades of a student whose accumulated grade is T, it is implied that we refer to a number such that, if all grades were equal to that number, then the total would also be T. For example, if the grades were 3, 4 and 5  (which add up to a total of 12), then the average would be 4, because if each grade were a 4, then the total would also be 12. This is the most common type of average or mean, called arithmetic. We usually refer to this kind when we say average without specifying which type.

The formula for calculating arithmetic means is well known and pretty straightforward. To obtain the arithmetic average of n numbers a, we sum these numbers and then divide by n:

The key to understanding the difference with the other kinds of means, and their applications, is realizing that in the grades example, as in every case that uses the arithmetic mean, the “accumulated total” is built through addition. But there are other situations in which there is a total that is the result of a different operation.

Take, for example, compound interest. Lets say we have an amount of money subjected to periodic interest, where the interest is 6% on the first period and 25% on the second one. The total interest is the yield after both periods, which is:

That is 32.5% (the dot in the middle stands for product). To understand why we multiplied those numbers, think of the each factor as the “amplification” for each period. To obtain the final value, we amplify the initial value with the first period’s interest, and then apply the second period’s amplification to that result. It yields the same result to multiply the amplifications first, thus obtaining a “total interest”, because the order of the factors doesn’t alter the product.

We may be interested in finding the average interest, meaning a percentage such that, if each period returned that rate, then the total interest would also be 32.5%. The arithmetic average of 6% and 25% is not the right answer (it equals 15.5%, which would produce a total of 33.4%) simply because the total, in this case, is not the result of an addition.

When gains are reinvested like in compound interest, the total is accumulated through a product, as we just saw. To obtain an average in a case like this, where the total is constructed by means of multiplication, we use the geometric mean (of those factors that are multiplied in the calculation of the total).

How is the geometric mean calculated? It is similar to the arithmetic one, but products are used instead of sums, because that’s how we construct the total in their case, and the nth root is used instead of dividing by n, because the total is equal to the average multiplied n times, instead of added up n times like with the arithmetic mean. Adding up n times is the same as multiplying by n, its inverse being dividing by n, therefore we use division for the arithmetic average. In the case of the geometric mean, multiplying n times is the same as  elevating to the nth power, which is the inverse of taking the nth root, thus we take the nth root for the geometric average. If it sounds too complicated nevermind, just believe me that taking the nth root makes a lot of sense here.

To summarize, the formula for the geometric mean, or average, is:

Back to the compound interest example. The geometric mean of 1.06 and 1.25 (which correspond to 6% and 25%) is:

Which corresponds to 15.1%. That interest applied consecutively for two periods would produce a total of 32.5%, the same as 6% followed by 25%. To put it short, we may say that 15.1% is the (geometric) average interest of a 6% interest followed by a 25% one.

The same can be applied to any rate of return that is compounded, such as stock returns when dividends are reinvested, and it works with negative returns too. For example, if a return of 15% is followed by a 10% loss (or -10% return), the average return is:

That is, 1.73%. Thus, two consecutive periods with a 1.73% return would produce the same result. By the way, in the formula we used .90 because it is the result of 1 minus .10, the latter corresponding to 10%; therefore .90 is the coefficient to use for -10%.

Although compound interests and returns are the most typical applications of the  geometric mean, it has other uses. For example, the geometric average of the length of the sides of a rectangle, is equal to the length of the sides of a square that has the same area.

In a future posting we will explain the remaining kind of average: the harmonic mean.

See also:  “Applications of the Geometric Mean” at U. of Toronto’s Mathematics Network

The purpose of the blog is to discuss investing in CEFs, and the perspective of specific funds. Your knowledge and opinion are more than welcome, so please share your comments and subscribe to the feed to receive update notices using your favorite reader.

Happy browsing!