Econometrics With R, Python and MATLAB

What is Econometrics?

Econometrics is a field in economics that applies statistical and mathematical methods to economic theories. It has become more relevant over the years as it helps economists quantify their economic theories and hypotheses. Econometrics helps economists test those theories by using statistical tools with mathematical equations. Therefore, it has become a crucial part of economic policymaking.

Econometrics usually involves establishing relationships between various economic variables. For that, economists use mathematical and statistical methods. Usually, economists must perform multiple calculations using complex models. Some economists use programming languages and other tools to expedite the process. These may include R, Python and MATLAB.

What is “R”?

"R" is a programming language that economists use for statistical computing and graphical representation. It offers an extensive list of statistical and graphical techniques. These include machine learning algorithms, time series, statistical inference, linear regression, etc. Furthermore, these are all tools that are an essential part of econometrics. Apart from econometrics, R is also prevalently used in other fields.

R is one of the most popular languages used by statisticians, researchers, analysts, and economists. Through it, they can extract, filter, analyze, visualize and present the data. It is also free to use and open-source, making it more accessible. It is among the top ten popular programming languages in the world. R has existed since the ‘90s but has gained popularity recently for its extensive features and runtime environment.

Base R contains a lot of functionality useful for econometrics, in particular in the stats package. In addition, there are many other econometrics packages available for free on the Internet.

What is Python?

Python is another powerful and high-level object-oriented programming language. It is the world’s most popular programming language. Like R, Python is also well-known among statisticians, economists, data scientists, and researchers. Similarly, most of the packages in R are available in Python as well, making it an all-in-one option for users. Apart from its usage for data processing, Python also has various other uses.

Python has existed since the ‘80s. However, the language has gained popularity recently due to its extensive list of libraries and ease of use. Most programmers recommend it as the best language for beginners to get started. Like R, Python is also open-source, making it available to the public. Most large companies in the technology industry use Python, including Google, Microsoft, Reddit, Mozilla, etc.

There exist many specialized libraries for performing econometrics studies in Python. Amongst them, Statsmodels is a frequently used package.

What is MATLAB?

MATLAB is a programming platform that focuses specifically on the needs of scientists, engineers, and data analysts. It allows users to make complex calculations, implement algorithms, create user interfaces, plot functions and data, and much more. It includes a vast library of mathematical functions for linear algebra, numerical integration, statistics, and differential equations.

MATLAB has some pre-programmed procedures that can help economists with their research. On top of that, there is a wide variety of open-source code available from other users online that is available to the public. Although it may not be as fast as Python or R, it is still the most famous program among high-level econometricians. Similarly, unlike Python and R, MATLAB is neither free nor open-source.

Econometrics studies can be performed by using the Econometrics Toolbox in Matlab.

Conclusion

Econometrics involves the use of statistical and mathematical methods to test economic theories. There are several tools or programming languages that can help econometricians. Usually, econometricians prefer R, Python, and MATLAB. All of these can help econometricians perform complex computations. Based on the needs and usage, each tool or language has its benefits and drawbacks.

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Tail Value at Risk: Formula, Definition

The Tail Value at Risk (TVaR) is a financial measure of a potential loss in a portfolio. Tail Value at risk uses the same statistical principles as the traditional value at risk with the only difference being that it measures an expectation of the remaining potential loss given a probability level has occurred.

Conceptually, tail value at risk is similar to Value-at-Risk (VaR), except it measures the maximum amount of loss that is anticipated with an investment portfolio over a specified period, with a degree of confidence

In this article, we'll first look at the basic theory behind the value at risk, and then we will introduce tail value at risk.

What is the Standard Deviation

Value at Risk is the measure of the downside or risky part of an investment. To be more precise, it answers this question: "What is the potential loss in a portfolio?".

To understand how Value at Risk works, we should first understand what a standard deviation is.

The standard deviation is one of the most commonly used tools for measuring variability and dispersion of data. If you are not familiar with the concept of standard deviation, you may want to check out "Standard Deviation and Variance: Statistics for Stock Traders" first.

Standard deviation can be used to measure both upside and downside variability in a portfolio. In order to get a better grip on this idea, let's look at a simple example below:

Suppose that you have a well-diversified portfolio, which you are tracking on daily basis. For the sake of simplicity, let's assume that this portfolio has 10 securities in it.

Daily returns are normally distributed with an average return of 0% and a standard deviation of 2%. So, one day you noticed that your overall return is -4%, instead of 0%. This is definitely not good news.

You have a look at the largest losses for each of the 10 securities and you notice that some of them are making significant contributions to your loss. Next, you looked into historical data and noticed that the securities that made a negative contribution to your portfolio on that day also did so in 50% of all cases. In other words, they have a downside correlation of 50%.

In order to assess the risk inherent in the portfolio going forward, you want to calculate how much money you may lose going forward.

So now let's find out how to calculate Value at Risk of a portfolio.

Calculating Value at Risk

Here is how you calculate value at risk

Value at Risk = [Expected Weighted Return of the Portfolio− (z-score of the confidence interval× standard deviation of the portfolio)] × portfolio value

​The standard deviation in portfolio returns is usually smaller than the individual securities' standard deviation since diversification helps to reduce dispersion. Also, you can expect that there will be more negative values than positive values in your tail distribution. This is because in reality the return distribution is not normally distributed (left-skewed).

Calculating Tail Value at Risk

Now, let’s examine what Tail Value at Risk is,

There are a number of related, but subtly different, formulations for TVaR in the literature. A common case in literature is to define TVaR and average value at risk as the same measure. Under some formulations, it is only equivalent to expected shortfall when the underlying distribution function is continuous at VaR(X) the value at risk of level alpha. Under some other settings, TVaR is the conditional expectation of loss above a given value, whereas the expected shortfall is the product of this value with the probability of it occurring.The former definition may not be a coherent risk measure in general, however it is coherent if the underlying distribution is continuous. The latter definition is a coherent risk measure. TVaR accounts for the severity of the failure, not only the chance of failure. The TVaR is a measure of the expectation only in the tail of the distribution. Read more

If X is the payoff of a portfolio that has f as the probability density function and F as the cumulative distribution function, then the left Tail Value at Risk can be expressed as follows,

Conclusion

As you can see Tail Value at Risk is very useful when it comes to measuring the downside risks of your portfolio. Although this method does have its limitations, it is definitely a step in the right direction.

Originally Published Here: Tail Value at Risk: Formula, Definition

Fair Value Hierarchy: Definition, Levels, Examples

Most companies use the historical value method of deriving their asset’s value. This process includes taking the asset’s cost and deducting any impairment and depreciation to reach the book value. The same method applies to deriving the value of liabilities. However, some accounting standards also require or allow companies to measure items at fair value.

What is a Fair Value?

The term “fair value” has various definitions in accounting and finance. It usually refers to the price a willing buyer and seller will pay or receive for an asset in an orderly transaction. The fair value of an item will also depend on the measurement date. Similarly, it may also be the price paid to transfer a liability in similar market conditions at a specific date.

In short, the fair value represents the market value of an asset or liability. However, there are several criteria attached to it. As mentioned, it requires the market participants to be willing to transact. It also needs an orderly transaction or one considered an arm's length transaction. The criterion for a measurement date is also crucial to establish a fair value for an item.

Sometimes, however, the fair value of an item may not be straightforward to determine. Since fair value is market-based and not entity-specific, there are several hurdles that companies may face. For example, companies may come across several fair values for a specific item from different markets. These inputs can confuse how to determine an item's fair value. For that, companies must use the fair value hierarchy.

What is the Fair Value Hierarchy?

The fair value hierarchy refers to the different classes in which accounting standards classify inputs. As mentioned, companies may come across several sources that provide information about an item's fair value. These values may differ based on the input they take. Similarly, the markets where these prices generate also impact the fair value.

The fair value hierarchy categorizes inputs used in fair value determination into three levels. This hierarchy provides the highest priority to Level 1 inputs. In case these inputs are not available, companies must use Level 2 inputs. Lastly, companies can use Level 3 inputs when the above two cannot be determined. Each of these differs from the others, as discussed below.

Level 1 Inputs

Level 1 inputs include quoted prices for identical items in an active market on the measurement date. For example, it may be a bid price for an asset or an ask price for a liability. Level 1 inputs are the most reliable evidence for fair value.

Level 2 Inputs

Level 2 inputs are directly or indirectly observable inputs rather than quoted prices. These may include the value of similar items in active or inactive markets. For example, a valuation multiple for a business unit based on the sale of similar entities is a level 2 input. After Level 1, level 2 inputs take priority.

Level 3 Inputs

In some cases, identifying level 1 and 2 inputs may not be possible. Therefore, companies must use level 3 inputs that are unobservable. It may include prices from a company's own data, adjusted for specific conditions. For example, cash or profit forecasts used to evaluate an asset would fall into this category. Level 3 inputs have the lowest priority in the fair value hierarchy.

Conclusion

Fair value is the market price for an asset or liability at a specific date between willing market participants. The fair value hierarchy identifies three categories for inputs. Usually, companies use level 1 inputs that have the highest priority. When level 1 inputs are not available, companies must use level 2 inputs. Lastly, companies can use level 3 inputs if none of the above can be determined. Level 3 inputs take the lowest priority.

Article Source Here: Fair Value Hierarchy: Definition, Levels, Examples

Using the Hurst Exponent and Stock Comovements for Pairs Trading

Pairs trading, or statistical arbitrage, is an effective market-neutral trading strategy. Usually fundamental or quantitative analysis is used in order to determine which pairs are suitable for trading. We have previously discussed several pairs selection methods based on quantitative measures such as stock cointegration, correlation, pair distances, etc.

Reference [1] introduced a new pairs selection method based on the Hurst exponent,

One of the critical steps in [Pairs] Trading is the pairs selection, but not too much attention has been given to the stock universe before pairs selection. In this paper, we have introduced a preselection procedure based on the stocks comovement measure through comovement functions based on comovement studies on physical particle systems. Therefore, portfolios with less volatile stocks have been selected, and it has been observed that, with this new modification, [Pairs] Trading is also profitable in periods of low volatility.

We find the paper interesting. Our comments are as follows,

• We’re of the same opinion that candidate selection is one of the most important steps in pairs trading. It is our understanding that the proposed selection method consists of 2 steps: i-selection of the underlying stocks based on comovements, ii-selection of tradable pairs based on the Hurst exponent.
• The pair selection method based on the Hurst exponent makes sense. Here the Hurst exponent of the weighted difference of the logarithm of prices is calculated, pairs are then selected and trading signals are generated directly using the difference. In contrast, other pairs selection methods make use of indirect measures such as cointegration or correlation.
• We think that it’s worth trying the pair selection method based on the difference of price, instead of the logarithm of price.
• The method for selecting the underlyings (step i) based on price comovements resulted in low-volatility stocks. This does not seem consistent with the empirical observation that pairs trading is considered an implicit short volatility trading strategy.

Regarding the last bullet point, the authors also noted,

However, on high volatility conditions, the strategy does not work as good. A plausible explanation of this phenomenon could be that, during periods with prolonged downward movements in the markets, volatility of the stocks is increased, and the model proposed in this paper is too slow to capture this faster change in the volatility of the preselected stocks.

Regarding the first bullet point, we believe that the pairs selection method can be improved by further performing, e.g., a robustness test in order to minimize divergence risks.

References

[1] J. P. Ramos-Requena, M. N. López-García, M. A. Sánchez-Granero, J. E. Trinidad-Segovia, A Cooperative Dynamic Approach to Pairs Trading, Complexity, vol. 2021, Article ID 7152846, 2021.

Originally Published Here: Using the Hurst Exponent and Stock Comovements for Pairs Trading

What is Risk-Adjusted Return on Capital

For a time, it was widely believed that the only way to determine how good an investment is, was by looking at its return. But in recent years, investors have come to realize that a high return doesn't always equal a good investment.

For example: if one company has a higher return than another but is also riskier - then the lower-returning but lower-risk company might be the better choice for many people. In order to account for risk when evaluating investments, some experts now use what's called "RAROC" or "Risk-Adjusted Return of Capital."

The idea behind this calculation is simple: you look at both returns and risks and calculate which investment will provide more money on average over time (taking into account the risks involved).

In this article, we will be looking at what is Risk-Adjusted Return on Capital (RAROC ) is, how it is calculated, and what the advantages and disadvantages are to using it.

What is Risk-Adjusted Return on Capital (RAROC)

Risk-Adjusted Return on Capital (RAROC) is a way of determining whether an investment's returns are reasonable, given the amount of risk it carries. The calculation for RAROC will reveal how much money an investor can expect to earn, per unit of risk that he or she takes. You calculate RAROC by taking the return of investment and adjusting it for risk.

How to Calculate Risk-Adjusted Return on Capital (RAROC)

Calculating RAROC is a fairly straightforward process. You take the estimated return of investment and divide it by the standard deviation to get a number known as "beta." The beta which you will be using in your calculation will depend on what type of risk-adjusted return on capital you are calculating.

RAROC = average return/ standard deviation

Riske-Adjusted Return on Capital can be used to show how much money an investor will earn, per unit of risk taken.

Risk-Adjusted Return on Capital (RAROC) Advantages

There are several advantages to the use of RAROC

1. It provides a good way of evaluating different investments with different risks
2. It allows you to make more precise comparisons among risky assets
3. By understanding the risk-return tradeoff, investors can better plan their portfolios and make smarter financial decisions. One of the biggest causes of bankruptcy is risk management
4. It enables you to estimate the value of a business
5. It allows you to make accurate decisions about the efficiency of your company

Risk-Adjusted Return on Capital (RAROC) Disadvantages

While RAROC provides a number of advantages, there are also several disadvantages to its use

1. Calculating returns for investment often involves looking at past performance, which can be misleading if you don't take into account the effects of inflation or other factors over time
2. Risk-adjusted return on capital only works in a theoretically perfect market, but not in a real-world setting where you can't assume that all risk is priced into an investment
3. Different measures for risk are used by different companies/individuals and come with their own sets of disadvantages
4. The market prices of risk can change quickly and unpredictably, which means that RAROC can become obsolete very fast
5. Risk-adjusted return on capital doesn't tell you what the returns are expected to be in the future

Conclusion

Risk-Adjusted Return on Capital (RAROC) provides a good way to get a snapshot of an investment's risk-reward profile. It allows you to compare the expected returns on different investments that are taking on different amounts of risk. Additionally, it can give you insight into business value by giving you a benchmark for estimating the present value of future cash flows.

Article Source Here: What is Risk-Adjusted Return on Capital

Salary Payable: Journal Entry, Calculation, Example

The accrual principle in accounting is a concept that requires entities to record transactions in the period in which they occur. This concept goes against the cash accounting method in which entities only account for cash transactions. However, the accrual principle does not consider the timing of the cash flows. There are several accounts that entities must maintain to follow this principle. One of these includes salary payable.

What is Salary Payable?

Salary payable is an account that entities maintain to record unpaid salary expenses. It represents the amount of liability that entities owe their employees. Usually, entities pay their employees after the month in which they work. However, as every month ends, entities incur salary expenses. Under the accrual principle, entities must record these expenses.

Entities usually pay off salary expenses after the end of the month. Despite the cash flows being on a different date, entities must record salary payable. Although named "salary" payable, the account may also contain various other employee-related expenses. These may include basic salaries, overtime, bonuses, benefits, and other allowances.

Usually, entities settle salaries payable within a few days. Therefore, the account does not often include any balances. However, when entities close their accounts and prepare financial statements, they must report salary payable. Since the liability gets settled within a few days, it will fall under current liabilities on the balance sheet. The related salaries expense will get reported on the income statement.

How to calculate Salary Payable?

Calculating salary payable is straightforward. Entities can calculate the amount by aggregating all employee-related expenses for a month. As mentioned, these will include employee salaries, wages, taxes, overtime, bonuses, and other related amounts. A sample formula for salary payable is as follows.

Salary Payable = Salaries + Wages + Bonuses + Employment Benefits + Overtime + Other Allowances

However, the above salary payable formula may not apply to every entity. Furthermore, the calculation is more complex in practice. Entities must calculate the salary expense for every employee separately. After that, they must aggregate those amounts to reach salary payable.

What is the journal entry for Salary Payable?

The journal entry for salary payable involves recording salary expenses and creating a liability. At the end of every month, entities must record this expense. Since there is no cash settlement involved at the date, increasing current liabilities is mandatory. Therefore, the salary payable journal entry will be as follows.

Dr Salary Expense

Cr Salary Payable

When entities settle the salaries at the start of next month, they must decrease the salary payable account balance. Therefore, this account also has another journal entry. The entry involves removing any remaining balances from the account that an entity settles. Nonetheless, the second journal entry for salary payable will be as follows.

Dr Salary Payable

Dr Cash/Bank

Example

A company, Kite Co., has over 100 employees. The total salaries expense at the end of each month for these employees is $100,000. Similarly, the company pays its employees on the 5^th of next month for their work. At the end of each month, Kite Co. must record a salary expense and payable. Therefore, the company must use the following journal entries.

Dr Salary Expense $100,000

Cr Salary Payable $100,000

On the 5^th of the next month, the company settles the entire amount through the bank. Therefore, Kite Co. must remove the balance from the liability account. The journal entries will be as follows.

Dr Salary Payable $100,000

Dr Bank $100,000

Conclusion

Salary payable is an account that entities use to record accrued salary expenses. This account exists due to the accrual principle in accounting. Salary payable includes various expenses, including salaries, wages, bonuses, overtime, allowances, etc. Once entities settle the amount, they must decrease the account balance.

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Earnings at Risk and Cash Flow at Risk

It's an important distinction to be made in the world of finance. Earnings at risk are when a company's future earnings are threatened due to factors such as unfavorable economic conditions or changes in consumer tastes. Cash flow at risk, on the other hand, is when a company's current cash flow is threatened by factors such as debt repayments and unexpected expenses.

Both the earnings and cash flow metrics are extremely important to shareholders. When a company's future earnings are in jeopardy, its long-term value is also affected. Thus, a shareholder may choose to sell the stock if the risk of diminished earnings is too high. However, this will have no impact on the company's current cash flow situation since it doesn't have any effect on the current cash flow that is coming in.

So now let's find out the key differences between earnings at risk and cash flow at risk.

What is Earnings at risk

Earnings at risk are earnings that can be threatened by factors such as unfavorable economic conditions or changes in consumer tastes. These factors may exist in the present and/or future.

A company's future earnings can be threatened when:

1. Unfavorable economic conditions occur in either their own industry, economy, or environment
2. Changes in consumer tastes affect a company's products
3. The costs of materials increase due to energy prices, inflation, or other issues
4. Product or service quality is diminished
5. New competitors enter the industry that causes competitive pressures
6. External factors such as bad weather, strikes, government regulations, etc affect production capacity

What is Cash flow at risk

Cash flow at risk is when a company's current cash flow is threatened by factors such as debt repayments and unexpected expenses.

A company's current cash flow can be threatened by

1. Expenses that are greater than the income stream
2. Increasing interest rates or an inability to borrow money at a reasonable rate
3. Inability to meet upcoming loan covenants
4. Inability to pay creditors on time
5. Downsizing initiatives that include significant layoffs or cuts in pay
6. Increased costs of production

What is the difference between Earnings at risk and Cash flow at risk

Earnings at risk are earnings that can be threatened by factors such as unfavorable economic conditions or changes in consumer tastes. Cash flow at risk, on the other hand, is when a company's current cash flow is threatened by factors such as debt repayments and unexpected expenses.

As you can see above that both earnings at risk and cash flow at risk are important to shareholders, but they are two different types of risks.

Earnings at risk affect long-term value since it primarily affects future earnings, whereas cash flow at risk does not affect the current cash flow situation.

Conclusion

Earnings at risk can be defined as earnings that can be threatened by factors such as unfavorable economic conditions or changes in consumer tastes. Cash flow at risk, on the other hand, is when a company's current cash flow is threatened by factors such as debt repayments and unexpected expenses. Both these factors are important to shareholders, but they are different types of risks.

Article Source Here: Earnings at Risk and Cash Flow at Risk

How Options Imbalances Affect Price Dynamics

As discussed several times, markets can be loosely divided into two regimes: trending, and mean-reverting. The majority of trading literature has been devoted to exploiting these market characteristics. Less attention, however, is paid to the explanation of their existence. They are often attributed to investors’ over-, underreaction and/or market inefficiencies.

Reference [1] looked at these market properties from a different perspective. It examined how the options gamma imbalances contribute to the market intraday momentum or reversal.

Recall that an option gamma is,

Gamma measures the rate of change in the delta with respect to changes in the underlying price. Gamma is the second derivative of the value function with respect to the underlying price.

Most long options have positive gamma and most short options have negative gamma. Long options have a positive relationship with gamma because as price increases, Gamma increases as well, causing Delta to approach 1 from 0 (long call option) and 0 from −1 (long put option). The inverse is true for short options

When a trader seeks to establish an effective delta-hedge for a portfolio, the trader may also seek to neutralize the portfolio's gamma, as this will ensure that the hedge will be effective over a wider range of underlying price movements. Read more

The article pointed out,

Establishing delta-neutrality may cause either return momentum or reversal depending on the sign and size of the imbalance vis-a-vis market prevailing liquidity. We find that a large and negative (positive) aggregated gamma imbalance, relative to the average dollar volume, gives rise to an economically and statistically significant end-of-day momentum (reversal).

It further showed that rebalancing of leveraged Exchange Traded Funds at the end of day also has the same effect on the price dynamics,

We compare this channel to the rebalancing of leveraged ETFs and find that the effect generated by leveraged ETFs is economically larger. Consistent with the notion of temporary price pressure, the documented effects quickly revert at the next day's open.

In short, both delta hedging and rebalancing of leveraged ETFs contribute to the stock market intraday momentum or reversal. The authors even managed to develop trading strategies based on these imbalances and they earned superior risk-adjusted returns.

We found the authors’ explanation of the intraday price dynamics plausible; however, we think that their strategies are rather difficult to implement.

What do you think?

References

[1] A. Barbon, H. Beckmeyer, A. Buraschi, and M. Moerke, The Role of Leveraged ETFs and Option Market Imbalances on End-of-Day Price Dynamics, 2021. https://ssrn.com/abstract=3925725

Originally Published Here: How Options Imbalances Affect Price Dynamics

Amortization Expenses: Formula, Journal Entry, Examples

What is Amortization?

Amortization is a method through which businesses lower the book value of their loans or intangible assets. It is similar to depreciation for assets. Both of these techniques help companies record the gradual decrease in an asset’s book value. However, depreciation only applies to property, plant, and equipment, or fixed assets. In contrast, amortization is only for intangible assets.

For loans, amortization helps companies spread out the book value into various fixed payments. Usually, this process involves using an amortization schedule to record principal and interest payments. In essence, amortization for assets and loans works similarly. However, the accounting treatments for both differ due to the underlying accounts involved.

How does Amortization work?

The matching concept in accounting requires companies to match expenses to the revenues they help generate. Therefore, companies must expense out the relative value of their assets for the period they provide means to make sales. This expense-out process usually comes in the form of depreciation. However, depreciation does not apply to intangible assets. Therefore, companies must use amortization to achieve a similar result.

For loans, amortization follows the same concept. It helps spread out the loan into various fixed payments for each period. Using amortization, companies can split these fixed payments into both interest and principal payment components. However, amortization does not apply to all loans, for example, credit cards or balloon loans.

How to calculate Amortization?

There is no specific formula for amortization. However, companies usually use the straight-line method to calculate amortization for intangible assets. The amortization formula under this method is as follows.

Amortization Expense = Asset’s Cost / Asset’s Useful Life

For loans, the amortization formula is more complex. However, most financial institutions and lenders provide an amortization schedule to borrowers. This schedule includes a calculation of all the interest and principal payments payable on a loan. Companies can use it to spread the loan over the number of total payments.

What are the journal entries for Amortization?

The journal entries for amortization differ based on whether it is for assets or liabilities. For intangible assets, the amortization journal entries are similar to depreciation. The value for the double-entry will depend on the amortization calculation based on the above formula. Nonetheless, the journal entries will be as follows.

Dr Amortization Expense

Cr Accumulated Amortization

For loans, on the other hand, the journal entries will differ. Every time a company makes a repayment, it must record amortization. It must also split the amount into the principal and interest components. As mentioned, this information is readily available from the amortization schedule. Nonetheless, the journal entries for the amortization of loans will be as follows.

Dr Interest Expense

Dr Loan (principal amount)

Cr Cash/Bank

Example

A company, Rage Co., owns software that costs $100,000. The company intends to use it for ten years. Therefore, the company will record an amortization expense for the software each year for its useful life. The annual amortization expense will be $10,000 ($100,000 / 10 years). Therefore, the journal entries will be as follows.

Dr Amortization Expense $10,000

Cr Accumulated Amortization $10,000

On the other hand, the company also obtained a loan from a financial institution. The loan requires Rage Co. to repay $20,000 annually, consisting of both interest and principal components. For the latest payment, the interest component amounts to $15,000. Therefore, the amortization expense journal entries for the loan will be as follows.

Dr Interest Expense $15,000

Dr Loan (principal amount) $5,000

Cr Cash/Bank $20,000

Conclusion

Amortization is a term that refers to the process of decreasing an asset or loan's book value. For assets, amortization works similarly to depreciation, but for intangible assets only. For loans, on the other hand, amortization spreads the loan payments over time. The accounting treatment for both of these will differ, as discussed above.

Article Source Here: Amortization Expenses: Formula, Journal Entry, Examples

How to Backtest a Trading System

Backtesting can become a key factor in the success of a system. Not even all experienced traders understand how to correctly implement a backtest, which often results in erroneous outcomes. If it is done correctly, we can expect some excellent results.

In this article, we are going to talk about the key factors to be considered for a backtest, and what steps should be followed in order to obtain great results.

What is a backtest

A backtest is generally understood as an evaluation of a trading system, where the historical price series data of security prices are used for testing. Every trader knows that it is virtually impossible to survive in this business without the ability to correctly and efficiently analyze a trading system.

Trading signals may be generated using many different techniques, among which we can name technical analysis patterns, algorithmic trading systems, as well as financial modeling methods. Regardless of what methodology has been used for generating trading signals, every system must be tested thoroughly before it is put into use.

A backtest is used for evaluating trading systems because it offers the possibility of using actual market data to test trading ideas without actually trading (which can become very risky). In addition, a backtest allows for testing a system as though its signals had been generated at that time, which makes it possible to generate reliable projections about how profitable the system may be in the future.

How to backtest

The following are the basic steps that should be followed in order to correctly implement a backtest:

1. Define system rules and variable definitions
2. Select a period for backtesting/simulation
3. Type in the starting capital
4. Set up a trading account
5. Run simulation/backtest and analyze results

First of all, system rules and variable definitions should be defined coherently. The next step is to select the period for backtesting. Even if the algorithm has been developed using long-term data, it is important to test it on at least one year's worth of historical price series data so that its behavior over various periods can be evaluated.

Once we have defined system rules and variable definitions, as well as selected the period for backtesting/simulation, we need to type in the starting capital - which is important because it will define initial equity and cash flows.

For example: If a system has been developed using $100,000 as its starting capital, and a 100% allocation of capital has been used for each trade, then the total amount of invested cash will be equal to $100,000. In this way, we need to type in the starting capital so that it can be properly taken into account when calculating equity growth/decline.

The next step is setting up a trading account. In this case, we need to define an account number as well as a broker from whom trades will be executed. Once the backtest is performed, all transactions generated by the algorithm will be reflected on a chart of a particular broker with which the system has been set up for testing purposes.

The final step before running a simulation/backtest is to define transaction costs. Many traders make the mistake of forgetting about transaction costs, which may lead to losing a big portion of trading capital due to the high fees charged by brokers.

Once all steps mentioned above have been implemented, we need to launch the algorithm/system that has been developed for backtesting purposes. The results can be analyzed in a variety of different ways. In addition, depending on the type of system being tested, it is possible to run multiple iterations to increase accuracy by obtaining more reliable results.

Conclusion

Backtesting is an important and integral part of developing a profitable trading strategy. It enables traders to estimate how their strategies would have performed historically without actually trading, which makes it possible to run market projections that define the expected profitability of a system for future use.

By following the steps described above, anyone can perfectly implement backtesting. In addition, by running simulation/backtest multiple times, it is possible to obtain more reliable results.

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