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Finance 101. Introduction to the World of Finance

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Finance 101

Introduction to the World of Finance

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Contents

Introduction ... 2

Interest rates ... 3

2.1. Time value of money ... 3

2.2. Interest rates ... 3

2.3 Components of Interest Rates ... 3

2.4 Default risk ... 4

2.5 Corporate borrowers ... 6

2.6 LIBOR ... 7

2.7. Fixed vs. Variable Interest Rates ... 7

Cash Flow calculations ... 9

3.1 Calculating future cash flows ... 9

3.2. Net Present Value ... 10

Annuities and Loan Payments ... 12

4.1 Annuity ... 12

4.2. Loan Payments ... 13

Foreign Exchange Conversions ... 15

Diversification ... 16

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Introduction

Hi my name is Angela and I am going to be taking you through this Introductory Finance course. I have been employed in Finance for 7 years, working for a large commercial bank. Prior to that, I obtained a Master’s Degree in Finance. I enjoy teaching and would love to share my expertise with you. So, let me walk you through the content of this course.

First, we will learn about the time value of money. Money today is more valuable than money tomorrow. This section is fundamental because we will introduce the concept of interest rates. I will show you, what the components are that form interest rates that you see in real life and how to optimize certain factors in order to obtain a more advantageous interest rate when you apply for financing. We will make the distinction between fixed and variable rates, and will learn how to calculate compound interest rates.

Once we have covered interest rates, we will be ready to calculate future and present cash flows.

We will know how to discount cash flows and will introduce the Net Present Value technique, which will help us study whether a certain project is viable from a financial standpoint.

Then we will start learning about annuities, which would allow us to calculate the monthly payment that is necessary for a 10-year mortgage loan with constant monthly payments. We will calculate a complete loan schedule.

We will dedicate one lesson in order to show foreign exchange conversion, which will clear any doubts about how to convert currencies once and for all.

And finally we will learn about the core principle that stays behind modern equity portfolio management theory – diversification. Regardless, of whether you want to become a professional investor or you need to allocate your own savings, you need to be familiar with the concepts of correlation and diversification.

You will even get a complete refund if you are not satisfied with the content of the course within 30 days of completing it.

As you can see, we have lots of work ahead of us. Let’s dive straight in and begin this journey together.

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Interest rates

2.1. Time value of money

The core principle of Finance is that money today is more valuable than money tomorrow. The rationale behind it is that money that we receive today has a potential earning capacity. This is why every person would prefer to receive money sooner rather than later and hence timing is one of the most important topics when we talk about money.

Let’s imagine that we will be paid $1,000 and we are offered to choose whether to receive it today or after 1 year. If we chose to receive the money today, we can go to the nearest bank and deposit it for a year. Given that the bank wants to attract such deposits, it is willing to pay interest on our money. Let’s imagine that the bank would pay us 3%, if we leave our money there for a year. In year 1, we will collect our initial $1,000 and on top of it, we will be paid 3% of $1,000. We will have

$1,030 in total. On the other hand, had we received $1,000 after 1 year we would have missed the opportunity to earn the interest of $30. The truth is that money today offers more opportunities than money tomorrow.

2.2. Interest rates

The interest rate is the cost of borrowing or the price that one pays for the rental of funds. There are different types of interest rates in our lives: mortgage interest rate, student loan rates, interest rates on investment loans, bonds, etc.

Interest rates play an important role in the economy for a number of reasons. If a person wants to buy a house and interest rates are too high, this could impede him or her from taking action. At the same time he might prefer depositing his savings in a bank because they would earn him a high level of interest.

A similar logic exists in the corporate world – high borrowing rates impede firms from investing in new projects.

As you can see, interest rates have a strong impact on the state of the economy.

It is also true that interest rates are influenced by the economy. During a period of stable growth, people are less concerned about depositing their money and similarly banks apply lower interest rates associated with their loans. When a crisis occurs, everybody is much more cautious and unwilling to lend their money, which results in higher interest rates.

Understanding the dynamics that interest rates have in different economic cycles is a key for making informed and successful financial decisions.

2.3 Components of Interest Rates

In this lesson we will talk about the components that form interest rates. Every type of interest rate that you are familiar with (mortgage, leasing, school loan, investment loans) can be disaggregated as the sum of five components.

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It is important to understand this topic well, because it enables you to be much more informed when negotiating with a bank, an investor or considering whether to make an investment yourself.

The building block of all interest rates is the real risk free rate, an interest rate that assumes no risks of default and simply reflecting the time value of money.

The second component is expected inflation. As time goes by, the market prices rise and the purchasing power of money is reduced. That is why interest rates contain a component that accounts for inflation and compensates for the reduced purchasing power of money. Such a component is added to the real risk free rate.

When someone borrows a given amount of money, there’s always the chance that he or she may not be able to repay the money because of bankruptcy or is unable to repay part of the loan. This is the default risk component. Every borrower has a different default risk profile and therefore this component is evaluated on a case by case basis.

The fourth component is called the “liquidity premium”. Some investments are highly liquid (US Treasury bonds for example) and have a low liquidity premium. Others are much less liquid. A liquid market gives investors options. If they need their money in a short period of time, they will be able to sell their investment on the market. On the other hand, if there isn’t a market it is much more difficult to exit at a given position. The investor will have to give a significant discount from the price in order to stimulate buyers, which will incur losses. That’s why a less liquid security must compensate its owners through a higher interest rate.

The fifth and last component that forms interest rates is the maturity premium. A maturity premium is added to those securities that have a longer duration. All else being equal, an investor would require compensation for the longer duration of his or her investment, given that he or she will be unable to use the money for a longer period of time.

The sum of these five components and a profit margin for the bank form the interest rates that we encounter on a daily basis. As we said earlier – a good understanding of these components allows us to have a much clearer idea and be stronger at negotiations.

2.4 Default risk

A very important part of the interest rate that is assigned to a particular borrower be it private or corporate is his or her default risk. Considering the components that form interest rates, the default risk is the only ingredient, which is unique for each single case.

The other four components are common for most loans or are attributable to a large category. They are more or less standard: everyone starts from the same level of LIBOR and faces the same risk of inflation. The default risk is different. It is specific for every borrower.

Every person, every corporation or even country carry their own default risk. And given that it is the only component that is strongly individual, this is where a bank concentrates when it tries to determine how much to charge you.

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The bank wants to assess:

a) How much it is going to lose if you default b) How likely it is that you will default

Let’s go a step further and introduce the following equation:

EL = EAD * PD * LGD

What we have here is: expected loss equals exposure at default multiplied by the probability of default, which in turn is multiplied by loss given default.

The first term EAD (exposure at default) shows what the amount is that the bank will risk if we default. These are usually the funds that it lent us and we still owe. The probability of default stands for the likelihood that the borrower will default. And then loss given default expresses what

percentage of the bank’s exposure will actually be lost. It is very rare that a bank loses its entire exposure.

A practical example might help. Let’s imagine that an individual buys a $300,000 house and finances the acquisition through a bank loan. The bank lends him or her $300,000 and he or she buys the house. After granting the loan, how much is the bank’s exposure at default (EAD)? Yes, it’s

$300,000. We are assuming that the person hasn’t made any payments. The probability of default is the likelihood that the individual would be unable to cover the payments of the loan. The higher the probability of default is, the greater the interest rate that will be applied to the loan. It depends on a series of factors that we will cover in a minute.

The third component of the equation is loss given default. That is the portion of the bank’s funds that will be lost if a default occurs. Banks never lose their entire exposure because normally they require guarantees from borrowers. For example, banks rarely lose more than 30% on mortgage loans because they have the right to resell the real estate property in order to get back their money.

This is not necessarily true during difficult market conditions. But despite that, we can conclude that the more guarantees that are given to a bank (under the form of mortgages, assets, pledge on shares, future income, etc.) the lower the expected loss percentage will be and hence the interest rate that it will charge you. And alternatively, if the bank has few or no guarantees the interest rate that it will offer will be much higher.

Several factors influence the estimation of a borrower’s probability of default:

- Earnings potential - Liquidity

- Past behavior - Quality of assets - External factors

Let’s go back to our case. The person who wants to purchase a house needs $300,000 in order to do it. The first thing that will be assessed by the bank is earnings potential. The bank needs to

determine whether he or she will earn enough money that would allow him or her to pay for the

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mortgage and cover living expenses. The larger the amount that remains after paying the mortgage the better it is, because this provides extra security to the bank. If the mortgage is for $300,000, the borrower will need to pay $2,500 per month throughout the next 10 years or $1,250 per month in 20 years. On top of that he or she will be charged interest, which means that the he or she will need to earn significantly more in order to pay mortgage payments and have sufficient funds remaining in order to cover living expenses.

Liquidity is important. A person may be rich in terms of total value of assets owned, but that same person may end up in trouble if he or she is unable to convert these assets to cash. Imagine that in our example, the person who wants to acquire a $300,000 house is paid on a project or per project basis. What if the payment of the next project is delayed by three months? He or she will miss three mortgage payments and will incur further debt in order to cover living expenses. This is why liquidity is important – it gives the borrower a cushion in case something does not go as planned.

A borrower with a record of paying debts on time and having a long-term home address should be offered a lower rate of interest than someone who misses payments or was unable to pay a loan in the past. So in our example, if the person applying for a mortgage loan has a good credit history and has been a good-faith borrower in the past, then it is much more likely that he or she will be

granted a loan and that the loan will have a lower interest rate.

Finally, we will consider the so called “external factors”, such as industry development and market risk. These do not depend on the borrower, but are related to his ability to repay his loan. If for instance he operates in an industry that is cyclical, this represents an additional risk that is accounted for in the interest rate that will be attributed to the borrower.

These are the components that influence the assessment of a borrower’s probability of default.

Once a bank determines its expected loss from the equation that we saw, it will know how much to charge in terms of the interest rate.

2.5 Corporate borrowers

The concepts that we saw before hold perfectly true for corporate borrowers as well. The main difference is that some corporations have access to more sophisticated loan forms such as syndicated loans, mezzanine loans, convertible loans and bonds.

Regardless of that, the interest rate is determined by the same parameters:

- Earnings potential - Quality of assets

- Guarantees in the form of mortgages, pledge on shares, other assets, etc.

- Liquidity - Credit history

- Industry of operation

Some corporate loans involve a great deal of insecurity and risk. Start-ups, growth and distressed firms seek loans at the so-called high-yield debt markets where interest rates could be as high as

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15% per year. The high interest rate makes it possible for such loans to exist, because even though the number of defaulting positions is substantial, the financiers are able to make up for that by charging more.

A corporate borrower that wants to improve its interest rate should present a strong case for it. The company should explain to its lenders that it has solid plans for the future, that its assets are

valuable and in good health that it will provide sufficient guarantees to the bank and it has sufficient liquidity that would allow it to continue to operate normally.

If the firm manages to convince the bank managers about these aspects, it will be able to get a lower interest rate than its peers.

2.6 LIBOR

LIBOR stands for London Interbank offer rate and is a benchmark rate used by large banks

worldwide in order to determine the cost of money when they charge each other for a short period of time. It is based on five currencies (US Dollar, Euro, British Pound, Japanese Yen, and Swiss Franc) and seven maturities (overnight, one week, one month, two months, 3 months, 6 months, and 12 months).

Given that many banks participate in the market it is very competitive and liquid, and is the standard rate against which others are compared and most loans are tied to. Due to the fact that it is very competitive, very liquid, its participants have a very low risk of default (they are very large banks), and it has only short-term maturities, the LIBOR rate approximates mostly the first building block of interest rates – risk free.

Now that we know what LIBOR is, we are ready to learn more about variable and fixed interest rates.

2.7. Fixed vs. Variable Interest Rates

A variable interest rate is an interest rate, which changes over time and does not remain constant. It is an interest rate that is tied to another market interest rate. Nowadays, LIBOR has become the industry standard that is used for most positions.

A variable rate is adjusted periodically and thus is not likely to remain the same throughout a loan’s life. It can increase or decrease, depending on the development of LIBOR.

Usually variable interest rates include a LIBOR rate plus spread. The spread is determined by the criteria that we saw before: inflation, default risk, liquidity and maturity.

A fixed interest rate on the other hand remains constant throughout the entire duration of a loan.

Even if market conditions change, the fixed interest rate does not change. The payments for the loan can be equal throughout its entire duration. Fixed rates are typically used for loans that have

duration of ten or more years. Most people prefer fixed interest rates, because they are averse to risk, but this is not necessarily the right choice.

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First of all, it really depends whether the current level of interest rates is low compared to at least 20 years of historical sample. If that’s the case it can be beneficial to lock in a fixed rate, but if this isn’t true, a variable rate is a viable alternative. Furthermore, fixed rates include some additional costs for carrying out transactions with derivative financial instruments (swaps), which allow a bank to fix the interest rate.

Historically, some academic studies show that variable rates tend to be less costly for borrowers in the long run.

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Cash Flow calculations

3.1 Calculating future cash flows

We already know that money today is more valuable than money tomorrow. We should bear this in mind when adding sums of money that will be received at different points in time.

Imagine the following cash flows.

Which one is preferable? Do we want to receive 100 in year 2 and 110 in year 3 or, alternatively, 100 in year 1 and 100 in year 2?

If we simply do the math, 210 is better than 200, so we should pick the first option. This isn’t necessarily true after we consider the time value of money. In Finance, we should never add sums of money without considering the timing when the cash flows occur. This is very, very important.

If I were to deposit $100 in a bank, I would expect the bank to compensate me for the right to use my money. Let’s say that the money will stay with the bank for a year and that after one year the bank will repay me the initial amount plus an interest of 3%. So we will have:

Future value = Present value x (1 + i),

Where present value is the amount we are depositing and “i” is the interest rate that the bank will pay us for depositing our money.

We would have:

Future Value = 100x (1+3%) = 103, after one year we will receive $103. What if we wanted to find the Present Value of a future Cash Flow? How do we find the present value of a cash flow that we will receive in the future? Starting from the equation Future Value equals Present Value times (1+i).

We can simply divide by (1+i) and will obtain that the Present Value equals Future Value divided by (1+i). When we account for the time value of money in this way, going backwards, we talk about discounting.

What if we wanted to make another deposit after year 1 ends? We would have 100 x (1+ 3%), which is the value at the end of year 1, and it will be deposited for another year, so at the end of year 2 we would have (1+3%)x100x(1+3%) = Future value at year 2.

The present value, 100, is equal to the Future Value divided by (1+3%)^2, so in general, when we need to discount a future cash flow that is “n” years from now, we need to divide it by (1+i) elevated to the “n”th degree.

Now that we learned this, we can go to our first example and calculate which one of the two cash flows has a higher present value. Here are the two sets of cash flows. The first one involves a payment in year 2 that is equal to 100 and another payment in year 3 that is equal to 110. In order to calculate Present Value assuming an interest rate of 10%, we need to use the formula that we have here:

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+

+

We will have 100, divided by (1+10%) to the second degree. We are elevating to the second degree because the cash flow is two years from now. Then, we will have 100 divided by (1+i) to the third degree because this is a cash flow in year 3. The Present Value that we will obtain from this equation is 165.3. It’s much lower than the simple sum of 100 and 110.

Now, let’s calculate the value of the other set of cash flows. We will have 100 discounted by one year plus 100 discounted by two years. We obtain that the Present Value of the second set of cash flows is 173.5.

+

As you can see, by discounting two sets of cash flows and obtaining their present value, we are able to compare them and decide which one is preferable. The selection of the discount rate is rather important in this calculation. For most people, it is their marginal borrowing rate – the interest rate which a bank would apply to them. If we are considering an investor, his discount rate will be the rate of return that he expects on his investments.

3.2. Net Present Value

Starting a new project requires a careful assessment of the cash flows that the project will generate in the future. We need to measure the approximate amounts and the point in time when they will be received or paid. This is critical for making an informed decision and is one of the main variables that help us decide whether a project is feasible or not.

Determining the value of a project can be challenging because of the time value of money. As we already know, a dollar earned in the future is not equal to a dollar earned today. Discounting cash flows and obtaining their present value is a way to account for this.

For example, if an investor wants to buy a given stock, he would first estimate the future cash flows that the stock would generate, discount those cash flows, and then add their present values. If the amount that is obtained is greater than the initial investment, the investment is feasible and will create value; otherwise it is not valid from a financial perspective.

Here is the Net Present Value formula:

Net Present Value is equal to the sum of Discounted Cash Flows minus the initial investment.

A firm plans to build a plant that will produce the following cash flows: 30 in year 1, 120 in year 2, 200 in year 3, 120 in years 4 and 5. After year 5, the plant will be completely obsolete and will have to be replaced. The plant costs 500 and the firm’s marginal borrowing rate is 10%. The financial

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director of the firm needs to assess whether to go through with the investment or not. Calculating the Net Present Value of the project would allow him to make an informed decision.

The initial investment doesn’t need to be discounted, that’s why we will start with the first cash flow of 30. In order to discount it, we need to divide it by 1 plus the interest rate, elevated to the first degree. The degree to which we are elevating depends on how many years from now the cash flow is that we are discounting. So, for example, the next cash flow will be elevated to the second degree because it is 2 years from now and so on:

NPV =-500+

This is how we obtained the discounted cash flows that will result from building the plant. We sum them with the initial investment that is necessary and this gives us the Net Present Value of the project. The sum is negative, which means that the project is not feasible and should be avoided.

The concept of Net Present Value is very important as it stands at the core of some fundamental financial techniques. It is applicable in many cases when a person or a corporation faces an important financial decision.

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Annuities and Loan Payments 4.1 Annuity

An annuity is a series of payments made at fixed intervals of time.

Why is this an important topic in our course? Well, it is important because many financial instruments and products are related to the concept of annuity.

Can you think of a financial product that involves an annuity? I’m sure you can. For example, monthly home mortgage payments are a type of annuity. Some insurance and pension payments are an annuity as well.

Whenever payments with a constant timing and amount are made, we are talking about an annuity.

Now, here is the formula for the Future Value of an annuity:

FV (i,n,R) = R x , where:

R is the amount of monthly or yearly constant payments and is the actuarial notation that is equal to:

where “i” is the interest rate and “n” is the number of periods.

Our task is to calculate the Future Value of a 5-year old annuity, where we will make constant payments of 100 each month throughout this 5-year period and where the interest rate will be 10%

on an annual basis.

We can do that very easily. We said that we want to calculate a 5-year annuity. Five years contain 60 months, and therefore we will have 60 monthly periods. Each month we will pay $100. The interest rate is 10% on an annual basis. We need to calculate it on a monthly basis given that all of our parameters are expressed in terms of months. I’ll divide 10% by 12 and will obtain the monthly interest rate. Now, let’s use the “FV” formula in Excel in order to calculate the Future Value of our 5- year annuity.

First, we have to select the interest rate, then the number of periods and finally the monthly

payments that we will make. The other two inputs are not compulsory. Let’s leave them as they are.

I’ll click “Ok,” and here’s the output of our formula – minus 7,743. We need to put a minus in front of the formula in order to obtain a positive value.

This is the amount that we will have in 5 years if we make constant payments of $100 at an annual interest rate of 10%.

Next, we will learn how to calculate the payment that will be necessary for a loan based on constant payments. Thanks for watching!

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4.2. Loan Payments

In this lesson we will address one of the fundamental topics in Finance – bank loans and the way their payments are structured. More specifically, I will show you how to perform calculations that are typically made for you by bank employees. It is a great idea to be prepared before your

conversations with bankers as this will put you in a stronger negotiating position. Furthermore, you will be able to distinguish between capital and interest payments, something that most people are not able to do.

We will consider a bank loan that involves constant monthly payments throughout its entire duration.

Let’s take our example from before. There is a person who wants to buy a house that costs

$300,000. After talking to some of his friends, and seeing several mortgage loan advertisements, he concludes that the current market rates are between 2% and 4%. So, he decides to make his

preliminary calculations by using a 3% rate.

He wants to repay the loan in 10 years by making equal monthly payments throughout these 10 years. Here is the million dollars question: how much will be his fixed monthly payment be in order for him to be able to extinguish the loan in 10 years?

There are two ways to calculate it: an easy way and a hard way. Which one do you choose?

Ok, we’ll use the easy way, but before that I want to explain you with a few words the mechanics that stay behind the hard way.

In our previous lesson, we saw the formula that allowed us to calculate the future value of an annuity. Well, here is the formula for the present value of an annuity:

PV (i,n,R) = R x , where:

R is the amount of monthly or yearly constant payments and is the actuarial notation that is equal to:

It is almost the same except for a small difference between the two actuarial factors “s” and “a.” The manual calculation shouldn’t be too hard after all because we have the inputs that are necessary:

the interest rate “i” and the number of periods “n.” We can easily solve the equations by substituting the numbers and solving for the only unknown – the monthly payment R.

In practice, things are simpler. Microsoft Excel allows us to calculate the equation much faster. The number of periods during which the loan will be repaid is 120, given that the person will make equal monthly payments for 10 years. The interest rate that he will have to pay for borrowing the money is 3% on an annual basis. Let’s divide it by 12 in order to obtain the monthly interest rate.

Ok. Very good. And, finally, the amount that will be borrowed is $300,000. We have all the

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necessary inputs that would allow us to calculate the monthly payment for the loan. The Excel formula for this calculation is “PMT,” as in payment. I will type it in the Formula Bar and will select each of the inputs… Ok. Our formula is ready. The borrower will have to make a monthly payment of $2,896 for 10 years in order to repay the loan.

Let’s go a step further and disaggregate what portion of each payment is interest, principle and how much is the remaining debt. Let’s create five columns – “period,” “payment,” “interest,” “principal”

and “residual debt.” We can improve the formatting of the columns a little bit... Ok. That’s better.

The first column will indicate the number of the respective payment. 1, 2, 3, 4 and so on, up to 120.

We already calculated the amount of each of the fixed payments. Here it is. I’ll link to the cell and then fix its references in order to be able to copy it to the last row of the table. Ok. Perfect.

Our next task is to disaggregate this payment in two parts: interest rate and principal. In the first period, the amount of interest that will be accrued is based on the whole amount of debt that is drawn, and given that no payments have been made, we have $300,000 times the interest rate, which equals $750. The difference between the payment and the amount of interest payments is the amount of principal that is repaid. In the last column, we can calculate the residual debt that

remains after this payment. Ok. Good.

Let’s do the same thing on the row below. I’ll multiply the interest rate by the residual debt (fixing the cell references of the interest rate). Then, I’ll take the difference between the payment that was made and the amount of interest. This is the principal that will be repaid in this period. Ok.

Let’s calculate the amount of residual debt by taking the difference between the amount that was due before this period and the residual debt after this period. Here’s our residual debt after period 2. We can copy these formulas to the last row of the table. As you can see, the residual debt at the end of the loan life is exactly 0, which means that we worked correctly.

This is how we can calculate an entire loan schedule. An exercise that allows us to plan better and understand exactly how much and for what we are paying.

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Foreign Exchange Conversions

The foreign exchange market is one of the most liquid and efficient markets in the world. Millions, if not billions, of people exchange currencies daily.

In this lesson, we will provide a few practical examples of how a given currency is converted into another currency.

Imagine the following table with quotes. Euro to USD means that 1 Euro equals “x” amount of dollars. The first currency is the one that we are expressing in terms of the second currency.

Remember that well. So, how many dollars we would have if we needed to convert 150 euros in dollars?

150 euro times 1.1 equals 165 dollars. Pretty easy, right?

Think of it as the following equation:

If we want to convert 150 euro we should simply multiply both sides of the equation, right?

= 165 USD

Let’s do the opposite case now. Imagine that you have $150 and you need to convert it into euros.

We will proceed in the exact same way. Starting from the equation:

We need to convert 150 dollars into Euros. Let’s divide both sides of the equation by 1.1.

Now we obtained how many euros do we get for 1 dollar. We can now multiply by 150 in order to find how many euros do we get for 150 dollars.

150 x

This is how we can convert currencies with ease. I hope that this lesson was useful to you. In case you have any doubts, you can always post a question or write us a message.

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Diversification

Very often financiers talk about the benefits of diversification. In this lesson we will explain what diversification is and why it benefits investors.

The main idea behind the concept of diversification is that one shouldn’t put all of their eggs in one basket.

A portfolio is a group of financial assets like stocks, bonds and investment projects that are held by a given investor. A portfolio of multiple investments will on average produce an improved risk- return combination with respect to a portfolio that contains only one or two positions.

In order to understand why diversification reduces the risk of a portfolio, we need to introduce the concept of correlation. Correlation is a statistical measurement that shows how two securities move in relation to each other. It needs to be between -1 and 1, where 1 is a perfect correlation. Perfect correlation means that the two securities will change in the same way. If one of them gains 5%, the other will gain 5% as well. If one of the securities loses 80%, the other will lose 80% as well. -1 on the other hand is the perfect negative correlation coefficient. If an investment gains 30%, its perfect opposite will lose 30% and so on. A correlation coefficient of 0 indicates that there isn’t any

correlation between the two securities, so their returns will be totally independent from each other.

There are, of course, securities that are positively correlated, but whose relationship is not perfect.

For example, a positive correlation of 0.7 suggests that if one security gains 20% the other will increase by 14%. They change in the same direction, but on a different scale.

Think of two companies. One of them is a food producer and the other is a logistics company. The correlation between their returns is 0.2. When the price of oil rises significantly, the price of the logistics company falls by 20%, given that this deteriorates its margins and volumes of business.

The increase of the price of oil will have negative consequences for the food-producing company too. Its price will fall by 4% as it will have to pay higher transportation costs, but we can agree that the logistics company will be affected more, given that its entire business lies on the cost of

transportation. The two businesses are positively correlated, but the negative event does not affect them in the same way. The correlation is positive but not perfect.

All else being equal, the lower the correlation between the components of a portfolio, the better it is, because a single negative event will pose a much lower threat for the entire portfolio.

Think of the following situation. You invest your savings in 1 company that is listed on the stock market. The company is called Enron and is a very, very large corporation that is known all over the world. Your expected return is 8%, which is more or less the average return of the market for the last 3 years.

Now imagine that a large scandal occurs and the company goes bankrupt in just a few days. You will lose your entire investment.

Let’s think of a second investor, who bought Enron stock in his portfolio, but held 29 other stocks as well. He expected the same return from all of his 30 stocks – the average market return for the past

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3 years. What is the amount that the second investor will lose if all 30 stocks had the same weight in his portfolio?

Yes. That’s right. He will lose only 3.33%. So, we can conclude that when an investor holds more stocks in his portfolio, he faces lower risk, while being able to maintain the same expected return.

Let’s go back to the example that we saw before. If the price of oil increases and the investor holds just 1 stock in his portfolio, the one of the logistics company, he will experience a loss of 20%. If instead he held more than 1 stock and the other stocks were with low correlation with respect to this event, he would lose much less. The lower the correlation between the assets in his portfolio, the less idiosyncratic risk he will be exposed to.

The saying that you should never put all of your eggs in 1 basket is perfectly true in the world of finance. An investor is able to reduce the risk of his portfolio by diversifying his positions and buying assets with low correlation.

References

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