Two key nuggets of knowledge will help you to get your head around the concepts and to answer the question correctly.

In this video blog, I’m going to take up practice question ID CSC 2 15-086. While this question doesn’t specifically refer to the efficient frontier, that’s precisely what it’s all about. You just need a well-trained eye to be able to see it. It asks how advisor Clara can make the portfolio more efficient? More specifically, what security should she keep? And by extension, which ones should she eliminate?

Now, full disclosure, standard deviation, and the efficient frontier are advanced concepts. I mean, entire textbooks can be devoted to them. Fortunately, unless you’re an analyst, you’re not required to understand them at a very detailed level, but you should have a solid understanding of them conceptually. So for the purposes of this question, two key nuggets of knowledge will help you to get your head around the concepts and to answer the question correctly.

Nugget numbe1, standard deviation, also known by the acronym SD, is considered a measure of risk. In simple terms, if the return of a security fluctuates or deviates greatly from year to year, it’d be considered riskier than one that doesn’t and would therefore have a higher standard deviation. Now, the higher the standard deviation, the higher the risk. Don’t worry, you won’t be called upon to actually calculate standard deviation. We’ll leave that to the math guys.

Nugget number 2, the efficient frontier considers two things, the level of risk as defined by its standard deviation and the expected return. Now, this is key. Number 1, the portfolio or combination of assets that would generate the highest return for a certain level of risk would fall on the efficient frontier. Number 2, any portfolio that would generate a lower return for that same or similar level of risk would fall below the other on the efficient frontier and is therefore considered an inefficient portfolio.

If, for example, a portfolio has a standard deviation of 3% and an expected return of 5% and another portfolio has a standard deviation of 6%, which means it’s riskier, but still only an expected return of 5%, which one would you pick? Well, in other words, from a risk versus return point of view, which one is the most efficient investment? Now, you’d likely think, well, they both have the same expected return. I may as well choose to keep the least risky one and eliminate the higher risk one. Does that make sense so far?

All right, let’s apply this to the question that we’re tackling. For learning purposes, let’s shuffle the securities in the table from the lowest standard deviation, which again means the lowest risk, to the highest standard deviation. Now it’s going to be so much easier now, and on a real exam I would jot it out like this if possible. Now each time we go up in risk, the return better go up accordingly. Otherwise, it isn’t as efficient. We should probably get rid of it in lieu of a more efficient investment. Make sense?

As we can see, security 3 has the lowest standard deviation of risk with an SD of 1%, and it has an expected return of 3%. Security 2 is the next riskiest with a standard deviation of 3%. So it involves more risk, but at least the investor is rewarded with a higher expected return of 5%. So really nothing stands out for me so far. So let’s move on.

The next riskiest security is security 1 with a standard deviation of 5%. So more risky than security 2, but notice it has the same expected return. Well, certainly from a risk versus return point of view, it’s less efficient than security 2, so we should probably get rid of it.

Next, let’s compare securities 4 and 5, which represent a lot more risk. Security 4 has a standard deviation of 9.8%, but at least the expected return is still pretty good at 7%. Security 5, though, is the riskiest with a standard deviation of 10%, but it also offers an expected return of a whopping 11%. Now, if we look at these two securities, we need to apply a little bit of logic here. Security 5 is only slightly riskier than security 4, but it provides an extra 4% in expected return. So with this in mind, we should eliminate security 4. So if we can eliminate securities 1 and 4, this means that we should keep securities 2, 3, and 5. So let’s select that answer. And, yes, we were correct.

So practice questions like this really serve to highlight the difference between merely reading the material and applying what you’ve learned with thought-provoking questions to ensure that you’ve grasped the concept well. Now, if you would’ve answered this question wrong, that’s okay, a lot of people might be in the same situation. But next time, I’m betting that you won’t.