# 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!