# You got mail: CFA Level I results….

Good afternoon everyone,

After yesterday night’s post on a somewhat soft topic, let’s get back to business with the CFA exam results I received today.

Let’s kill the suspense straightaway! I am delighted to be able to say that I passed my Level I exam. That’s great news and it’s a huge relief as I am always unsure of the outcome of this kind of exams.

The CFA institute does not provide you with your exact score but rather gives you a range of success ratio for each specific topic.

Unsurprisingly, I didn’t manage to do more than 50% in Economics as the topic is very broad relative to the number of questions that are actually asked, but I’ll try to work on that a bit during this summer. That was for the weak range.

Then comes what I’d call the middle range with 51% – 70% success ratio within which my scores in Derivatives, Fixed Income and Quantitative Methods all lied. That might come as a surprise for some of you as they should be some of my strongest topics, but I think it can be explained by the kind of questions that were asked during the exam. Indeed, questions in these topics were not very quantitative and sometimes relied on terminology or specific definitions. I guess this is where I lost my points because I am fairly confident of the computations I performed.

My scores for the remaining topics ended up in the upper bracket with more than 70% success ratio. I am pretty happy about this because it seems that I got the feeling right in Ethics which is a topic which requires practice, practice and… practice. I’m particularly satisfied to have obtained such a score in Accounting as it is a key topic in the Level I curriculum because of the number of question being asked about it in the exam. I must say, I felt most Accounting questions were really doable since difficult topics such as deferred tax assets/liabilities were represented with relatively easy (or at least quite straightforward) questions.

To sum up my Level I experience, and as I had the time to look back at what I did before they exam and how it paid up, I would like to highlight the importance of having the Schweser notes and particularly the Schweser QBank (the tool which contains tons of practice questions for each topic). Practicing questions definitely looks to be the right way to be successful in the exam, at least for people with a professional activity during the day who have less time available for the exam. Focusing on the key exercise types where easy points can be made by remembering a formula (or at least a process) proved to be a very useful technique at the exam as it secures points, saves time and provides confidence.

I would like to end this post with a word of thanks for those who supported me during my journey towards this CFA Level I exam success. First of all, I would like to thank Unigestion, the company I work for, for trusting me and supporting me as well as providing me with some extra training time. In particular, I would like to thank Pierre Bonart who encouraged me to start this curriculum and who provided me with great advises and showed so much support. I would also like to thank my family and my girlfriend Sarah for helping me mentally and for standing by me during the difficult and stressful pre-exam days and for their great understanding during the whole preparation process.

Finally, I want to underline that I do know that the road to the CFA is far from over, and that this was maybe the easiest step towards the designation. I will be back with more CFA content, this time concerning Level II material, when I receive the new set of notes for the next challenge in June 2013.

# CFA Level I: that was it.

Hi everybody,

I finally took the Level I exam of the CFA curriculum yesterday. I take the opportunity to express my feelings about how my studies went and what my feelings were about the actual exam. As a matter of fact, I cannot disclose any of the specific questions I (and the other candidates) encountered in the real exams, because of the strict CFA exam policies.

## The Level I curriculum

I believe the main thing I will remember about the curriculum is its diversity and its broad coverage of the financial world. Let me just restate the different sections of the curriculum:

• Ethics
• Quantitative Methods
• Economics
• Accounting
• Corporate Finance
• Portfolio Management
• Equity Investments
• Fixed Income Investments
• Derivatives
• Alternative Investments

I liked the fact that I think that you will find some challenges even in the section you think you already master. For example, I knew most of the subjects presented in Quantitative Methods, but still a few things were presented in a different way, a way that I didn’t face during more mathematical studies. These new approaches lead to surprising questions; but I think I mastered them quite quickly.

I really learnt a lot in terms of broad markets, you have an explanation of the different types of asset classes and it’s not only about valuation, it’s also about how it works, what kind of instruments should be used given a specific situation, so that’s great and it really helped me reading some articles and during my fund selection duties.

Economics was a difficult section for me. As a matter of fact, the program is huge compared to the number of questions that is allocated to this topic. Hence, as I don’t have a degree in Economics (and these economics are not approached really mathematically), it was really all about damage limitation.

For accounting, I believe some questions are really approachable. EPS and DuPont analysis help you get at least a few questions right without hesitation; there is not debate or understanding really involved as you will get it right if you know the criteria. However, I believe there are some questions that you can hardly answer if you are not doing accounting in your daily job.

## The exam

About the exam itself, I have mixed feeling about how it went, and I’m not really sure of the outcome, but I’m never confident about an exam so we’ll see. As I mentioned I cannot discuss about the content, however I can say that the organization was, as expected, very strict. I saw people not being able to take the exam because they didn’t have a valid passport. I even had to show an additional piece of ID because I was much thinner on my passport picture than I am now! But if you’re just reading your e-mail and the exam policy on the CFA Institute website, you’ll be fine really.

That’s it for today, I’m really happy this is over and I will be back with more content on quantitative finance soon!

# CFA Level I: DuPont Analysis

Hello again,

Back to reality after the events of last week in the Premier League and last night in the Champions League with some … accounting, in a sense.

The CFA Level I curriculum has a lot of question about ratios and a lot of questions ask how the return on equity ROE is affected by different properties of the firm. Let’s first look at the basic formula for ROE:

$$\text{ROE} = \frac{\text{net income}}{\text{equity}}$$

Ok that’s quite intuitive, but it doesn’t really provide a lot of insight on how different properties of the company will affect the ROE. This is where DuPont analysis is useful. The idea is pretty simple, we will introduce factors in the formula which will cancel out each other but will help us understand what is happening underneath the ROE. Let’s look at the traditional DuPont equation:

$$\text{ROE} = \frac{\text{net income}}{\text{sales}}\frac{\text{sales}}{\text{assets}}\frac{\text{assets}}{\text{equity}}$$

We now have a multiplication of three ratios, respectively:

• Net Profit Margin
• Assets Turnover
• Leverage Ratio

This decomposition is very useful to answer questions. Indeed, you know that if ROE is low, it is because either the net profit margin is poor or because the asset turnover is poor or because the firm is under-leveraged.

An easy way to remember the formula is just to remember two of the terms (for me, I remembered net profit margin and financial leverage); the third term can be found again using simple math.

Now there is an extended DuPont equation which further decomposes the net profit margin as follows:

$$\text{ROE} = \frac{\text{net income}}{\text{EBT}}\frac{\text{EBT}}{\text{EBIT}} \frac{\text{EBIT}}{\text{sales}} \frac{\text{sales}}{\text{assets}}\frac{\text{assets}}{\text{equity}}$$

Again, you see ratios coming up:

• Tax Burden
• Interests Burden
• EBIT Margin
• Asset Turnover
• Leverage Ratio

You can perform an analysis on how the ROE would change by having a look at each ratio.

Finally, there is an interesting thing about ROE that also comes up in the Corporate Finance topic of the CFA Level I curriculum: it is related to growth and dividend payout ratio. Indeed, we have the following relation:

$$\text{g} = \text{ROE} \cdot (1-\text{dividend payout ratio}) = \text{ROE} \cdot \text{retention rate}$$

This is quite simple to understand and it allows you to solve questions when the growth rate is not explicitly given. The growth rate is in fact determined as the amount of return on equity that is not given away to shareholders as dividends. This amounts allows the company to grow and produce more net income in the following period.

That’s it for today. I’ll try to add more content soon!

# CFA Level I: Hypothesis Testing

Good evening,

As I keep practicing towards the Level I exam, I want to finish my review of the  Quantitative Finance material. This post will hence be the follow up of my previous post. I will here discuss how you test a hypothesis on some statistical measure.

## General Concept

The main concept is as follows, you make an initial hypothesis which is called the     null hypothesis, $H_0$, and which is the statement you want to reject. If $H_0$ is rejected, we hence can accept the alternative hypothesis $H_a$. Of course in statistics, you can never be sure of anything. Hence, you can only reject the null hypothesis with a certain confidence level $\alpha$. It is important to understand that if you can’t reject the null hypothesis, it does not mean that you can accept it! Hence, rejecting the null hypothesis is more powerful than failing to reject it. So, if you want to prove some statement, you should test for its opposite as the null hypothesis; if you can reject it, then you can accept the alternative hypothesis which is your original statement. A test can either be one-tailed or two-tailed, depending on what you want to test.

## First example

Let’s take a simple example: you measure a sample of the returns of the S&P that you assume to be normal. You measure a sample volatility $\mu_s$ and a sample standard deviation $s$. By the central limit theorem, we now that the estimate of the mean follows a law $\mathcal{N}(\mu_0, \frac{\sigma^2}{n})$ where $\mu_0$ is the population mean and $\sigma$ is the population standard deviation. Now, you cannot use your measure $\mu_s$ to say that you found the true population mean, because it’s just a sample statistic. However, what you can say is that, given the fact that you found the sample statistic $\mu_s$ and a given confidence interval $\alpha$, it is highly improbable that the population mean $\mu_0$ was equal to some value $x$. Hence the null hypothesis is $\mu_0=x$.

Let’s assume that you found that $\mu_s=0.1$, $s=0.25\%$ and $n=250$.  You want to show that $\mu_0 \neq 0$, so you null hypothesis is $\mu_0 = 0$ and with a significance level $\alpha=5\%$. You can compute the z-statistic as follows:

$$z= \frac{\mu_s-\mu_0}{\frac{s}{\sqrt{n}}} \sim \mathcal{N}(0,1)$$

Now if $\mu_0$ was equal to 0, you know that there is 5% chance that the estimate $\mu_s$ would lie outside the range $\mu_0 \pm z_{2.5\%} = 0 \pm 1.96 = \pm 1.96$ (because the sample statistic can lie on both side of the distribution). The z-statistic was computed at 6.33, which is more than 1.96, so you can reject the null hypothesis $\mu_0=0$ and accept the alternative hypothesis $\mu \neq 0$.

This was a two-tailed hypothesis. One-tailed hypothesis would be looking at only one side of the distribution: $H_0 = \mu_0 \geq 0$ or $H_0 = \mu_0 \leq 0$. As a rule of thumb, you can remember the the null hypothesis always contains the “equal” sign.

## P-values

The p-value is the probability (assuming the null hypothesis is true) to have a sample statistic at least as extreme as the one being measure. You compute it by look at the test statistic (6.33 in the previous example) and you find the probability (using the Z-table) that a test statistic can be above that value (and you multiply it by 2 if it is two-tailed). In this case, the p-value is very close to 0. Now, if the p-value of the test statistic is below the significance level of the test, you can reject the null hypothesis. This is useful if you want to discuss statistics without having to impose a certain significance level $\alpha$ to the reader; you can just display the p-value and let him decide whether it’s good enough or not.

There are some other hypothesis tests presented in the curriculum, but this is the main framework to remember. It’s pretty easy, and it allows you to score a lot of points in the quantitative finance part of the exam.

# CFA Level I: Buying stocks on margin.

Hi everybody,

Today I’ll try to write several posts on the different things I looked at during my time in Tel Aviv, which will come to an end very early tomorrow morning.

I will also setup soon a page where I will display my progress in terms of score percentage in my practice sessions as time flows towards the exam day.

The posts I will be adding to the blog mostly concern things you can learn quickly and that will allow you to score easy points in the exam by just applying the formula. The first one of this series has actually been written already, it was concerning Basic and Diluted EPS.

In this post, I will talk about buying stocks on margin. This might seem at first glance quite complicated, but it’s in fact a quite simple concept. When you buy stocks, brokers will allow you to buy them on margin, that is, they will allow you not to deposit the full amount you would require to buy the stocks and lend you to rest of the amount for a given interest rate $r$. This allows you to gain leverage on the investment. As always when it comes to leverage, it’s a double-edged sword; your gains will be magnified by the leverage effect, but so will your losses.

Let’s take an example which I will you throughout the post: I want to buy 100 stocks priced today at 10. Assuming my broker allow be to buy using an initial margin $m_i$ of 40%, I will have to deposit only $100 \cdot 10 \cdot 40\% = 400$. Now if the price in a year is 11 (that is, a return of 10%) and I decide to sell the stock, I will make a profit on the stock price of $(11-10)*100=100$. The simple case assumes that the broker lend my the extra $600$ for an interest rate $r=0$. My return on the investment is hence $\frac{400+100}{400} = 25\%$. This is much bigger that the initial stock return. Another way to compute this simple case is to compute the leverage ratio $LR=\frac{1}{m_i} = \frac{1}{0.4}=2.5$ and then multiply it by the return of the stock to get the leveraged return: $10\% \cdot 2.5 = 25\%$. Okay so that’s easy. The CFA Institute might be willing to make this a bit more complex by adding dividends $d=0.5$ to the stock, and setting $r=5\%$ (the values are taken as examples). The reasoning is still the same:How much was I required to invest? still 400. How much do I get from the increase in price? still 100. How much dividend do I get? $100 \cdot 0.5=50$. How much interests do I have to pay to the broker? $100 \cdot 10 \cdot (1-40\%) \cdot 5\% = 30$. So you can compute the return on the investment as follows: $$\frac{400+100 + 50 – 30}{400} -1 = \frac{520}{400}-1 = 30\%$$ Finally, the last typical question is about margin calls. The idea is that the broker (and the regulators) would want to make sure that you are able to pay your debt if the investment goes bad, as you did not deposit the full amount of the investment. Hence they have a maintenance margin $m_m$ which is a “limit” under which they do not want your margin to go. The price under which you will get a margin call (that is when the broker requires you to refill the account back to the initial margin requirement) is computed as follows: $$P_0 \frac{1-m_i}{1-m_m}$$ So if we assume in our example that $m_m=25\%$, then you will have a margin call when the price reaches $10 \frac{0.6}{0.75} = 8$ So, with basically one formula to remember, you will get some very easy points in the exam!