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Financial Investment and Corporate Risk Analysis

Course Name: Corporate and Financial Risk Management

Module Number: 849G1

Module Name: Financial Investment and Corporate Risk Analysis

Question 1

Financial Risk is a broad field of study that can cover anything from the impacts of interest rates to how the credit markets work. The range of topics covered in this module is equally wide and diverse. Even within a single topic, there can be several different ways to provide an answer to the same question. In this module, I acquired skills in bond pricing, calculating credit risk and the Net Present Value, testing Granger causality, time series analysis, and forecasting using Autoregressive models (AR), Moving Averages (MA), Auto-regressive-Moving-Average model (ARMA), Auto-Regressive Conditional Heteroscedasticity (ARCH), and GARCH models.

In statistics and econometrics, a time series model is a type of statistical model used in analyzing temporal data series. Time series analysis refers to a set of techniques for examining data across time to extract useful statistics and other information from a collection of data features of the information. The time series models include Autoregressive models (AR), Moving Averages (MA), Auto-regressive-Moving-Average model (ARMA), Auto-Regressive Conditional Heteroscedasticity (ARCH), and GARCH models. Time series models are often used to model a response variable with an underlying process that evolves over time to assess and forecast the impact of interventions at future points in time. A moving average (MA) is a type of time series model that displays the average of the data points for a brief time period. A moving average is a simple statistic that helps identify the trend in a data set, typically removing short-term fluctuations.

On the other hand, Auto-regressive (AR) models are mathematical equations for forecasting data that use a long-term history to predict the future. When looking at time series, it is important to think about what is driving the initial conditions to predict where the data will end. There are many different types of autoregressive models, but they all work by using past values and their relationships with current values in order to make predictions. An ARMA model has an autoregressive component (a term in regression analysis) and a moving average component (an integral part of filters). Essentially, this is a model used to predict future values based on past values, which are influenced by past values from before and current values (Zhang et al. 2014).

ARCH (autoregressive conditional heteroscedasticity) is a mathematical model for analyzing and forecasting time series dynamics. ARCH modeling is a flexible model that closely reflects real markets that is used in the financial world to measure risk. The GARCH model is an ARCH extension that includes both the dynamic scale and the autoregressive component. GARCH processes use past square recognition and past variance to account for current differences. Because of their efficiency in modeling return on assets and inflation, GARCH systems are frequently financially sound. Calculating predictive failures and improving continuous quality.

From the above topics, I have been able to model and predict data using the above models. By using ARCH and GARCH models, I am able to predict the volatility and risks involved in stock prices.

Question 2

Altman created the Z-rating version, that's a numerical components that predicts whether an employer might be in trouble inside the subsequent two years. The Z-score method is used to determine whether a company is likely to fail in the next two years. Several times, the model has been shown to be a reliable predictor of extinction (Tung & Phung, 2019). According to the study, the model predicted a fall two years ahead of time with a 72 percent accuracy rate and only a 6% false positive rate. The 10-K data is used in the Z-score model, which is based on five key financial ratings.

The Altman- Z score is given by

Altman Z-Score = 1.2A + 1.4B + 3.3C + 0.6D + 1.0E

Where A to E denote the five major financial ratios:

A- Working capital/ Total Assets

B- Retained earnings/ Total Asset

C- Earnings Before Interest and Tax/Total Assets

D- Equity Market Value/Total Liabilities

E- Sales/ Total Assets

The average visual deviation from the definition is calculated using the Z-score model, which is a mathematical calculation. With accordance with Altman Z-rating, the lower the Z-score, the more likely the business enterprise will fail. A Z-rating of 1.8 and below, shows that the corporation is experiencing financial difficulties and is prone to going bankrupt. A score of 3 or higher, however, shows that the organization is healthful and could no longer are seeking liquidity.

For example: Using a case of GM motors, 2015 data.

 

Since, the Altman Z-score for GM motors is above 3.0, there is an indication that the company is highly unlikely to go bankrupt in the near future.

Question 3

Homes are the largest asset that most people will ever own. In Australia, Canada, China, Ireland, and the United States, house prices have more than doubled in the last 20 years. House price growth has decelerated to less than 10% per annum in some countries, but it is still at a far higher level than during the pre-bubble period of 1985 to 1995. Most house price movements have been driven by demand. Many factors affect the factors that affect demand for houses. If a country has low-interest rates and the banking system is well regulated, then people who would otherwise borrow to buy a house will do so from banks or superannuation funds instead (Geng, 2018).

The main driver of housing demand is income growth. At a minimum, people want to keep up with inflation, but in most markets, they want to keep up with real income growth as well as capital gains. The Federal Reserve's 25-year old policy of holding interest rates at 1% has contributed to the increased wealth and increased demand for housing in America, Australia, and Canada. The typical house price cycle is dominated by peaks and troughs caused by demand factors. When supply outweighs demand badly, as it did in the 1980s and 1990s, then prices fall rapidly (Savva, 2018). In Australia, there was a serious shortage of dwellings in many markets during the mid-1980s and a severe oversupply of houses in the late-1990's. The Federal Reserve increased interest rates from 6% to 15% in the early1990s because it thought that was necessary to bring up inflation. It failed to act more aggressively, and this resulted in a prolonged house price boom from 1995 to 2005.

Question 4

A retail business will have variable profit depending on a number of factors that can change randomly. These factors include the cost of supplies, natural disasters, and changes in the economy. The better luck this company has with these variables, the better its profit margin will be.

Simulating the profits using excel, the histogram plot below was obtained. The histogram below indicates that the data is normally distributed since it is bell-shaped. The assumptions involved in a normal distribution include; homoscedasticity, linearity, and no multicollinearity.

 

Question 5

Hedge funds are an investment vehicle that provide an opportunity for investors seeking both capital appreciation and income. This fund is typically offered as a mutual fund or exchange traded fund. Despite this option, the vast majority of trades are executed as a long-only portfolio. Hedge funds were originally designed to mitigate downside risk in a portfolio by hedging out the fluctuations in market prices with positions taken on financial instruments such as equities, bonds, and currencies; today, many hedge funds carry positions on not just one but all three asset classes (Connor & Woo, 2004). Hedge funds typically invest in a diversified portfolio of securities, with an emphasis on investment strategies that have been proved to be successful in the past. A hedge fund's success is measured by the compound return on invested capital (ROIC). The increasing popularity of hedge funds has led to a steady rise in competition among hedge fund managers and an increased reliance on leverage and leverage ratios. Hedge funds are usually very liquid, since fund managers can readily sell or short a position near the current market price. However, there are also hedge funds that are illiquid.

Another other kind of investment that takes benefit of market opportunities is hedge price range. These investments typically have a higher initial investment than maximum different sorts of investments and are only to be had to authorized investors. That is due to the fact the SEC regulates hedge finances on a far smaller scale than other funding vehicles like mutual finances. Maximum hedge funds are illiquid, this means that that traders must preserve their investments for a long time and that withdrawals are regularly restricted. As a result, they appoint a selection of techniques to ensure that their buyers receive adequate returns. Capacity hedge fund traders, alternatively, should be privy to how these investments generate profits and what sort of hazard they are taking when buying this economic product.

To strive to produce active returns for their clients, hedge funds use a variety of techniques. There are many different strategies used by hedge funds, and it is wise to familiarize yourself with some of them. Long/short equity trading is short-term trading that is based on market pricing discrepancies; when a stock rises, while other stocks fall, this can form an opportunity for investors who are then able to sell their position before the price gap closes. Since each individual hedge fund has its own risk profile and processes investing in securities through different industries and asset classes, what works for one won't necessarily work for another. A pair-and-trade variance is a strategy in which investors buy and sell two competing businesses in the same industry based on their related values. Low-risk bet on the manager's stock selection abilities.

Unlike market-neutral hedge funds' long-/short-term strategies, they aim to be fully exposed to the market, meaning shorts and longs have the same market value. Stock options are thus a unique source of management compensation. This strategy is less risky than long-term bias, but the return is less predictable. Investors in hedge funds are increasingly looking for less volatile returns. The mainstream approach of aiming to beat the performance of an index while minimizing volatility is not as popular with fund investors in recent years. The "market neutral" strategy has become increasingly popular among hedge funds and has been prompted by investors’ desires for alternative investment opportunities to manage risk. A market neutral strategy means the value of a position does not change whether the asset classes are going up or down, therefore hedging risk and mitigating downside volatility.

Market neutral strategies are an alternative to a traditional long/short hedge fund. The term "market neutral" refers to the neutral return profile of the strategy, which is achieved by investing in assets that move opposite to one another, so returns from one asset class offset the losses from another. Market-neutral hedge funds aim for positive returns in all market conditions. Other strategies include, quantitative, short-only, fixed, global Macro, Event-Driven Arbitrage, Merger Arbitrage, and Convertible Arbitrage strategies.

The benefits of investing in hedge funds include, the increased profits in rising and falling markets are among, reduced risk and volatility in balanced portfolios. There are a variety of investment strategies to choose from, and top investment managers are in charge. However, the losses involved in investing in hedge funds can be substantial, and there is less liquidity than with traditional mutual funds. Furthermore, the money is locked up for long periods of time, and the leverage can exacerbate losses.

Question 6

The market for equity futures is one that has seen a lot of growth in recent years, especially for investors betting on the direction of the overall market. Long and short equity hedge funds allow people to buy into either long positions or short positions on stocks, and profits from these trades are passed to their investors.

If Apple Inc. appears to be undervalued in comparison to Microsoft, a pair trader might buy $100,000 from Apple Inc. and sell $100,000 in Microsoft shares. The investor has no exposure to the rest of the investor market, but if Apple Inc. outperforms Microsoft, the investor will benefit regardless of the market as a whole. Assume Microsoft increases by 15% and Apple Inc. increases by 22%. The merchant made a profit of $ 7,500 by selling Apple Inc. for $ 122,000 and cover Microsoft's briefcase for $ 115,000. If Microsoft falls 30% and Apple Inc. falls 23%, you could sell Apple Inc. for $ 77,000, cover your Microsoft short with $ 70,000, and make a $ 7,000 profit. If the trader is wrong and Microsoft outperforms, they will lose money.

Question 7

Financial risk is the possibility that financial assets will lose value. Analyzing financial risk with more than one factors can be difficult and can cause confusion, which makes it harder to understand and manage. The three most common factors to consider when analyzing financial risks are: currency rates, interest rates and inflation. It is also important to determine which events will affect the business in different ways than others. Inflation is a major factor that affects a company's cash flows and profitability. Interest rate changes will affect the company's cost of borrowing and servicing debt. Foreign exchange rates affect income from operations as well as the value of its net assets, equity and liabilities.

When analyzing risk with these factors, it can be difficult to understand the potential effects on individual categories of financial risk, such as foreign exchange risk or inflation risk. Failing to understand what affects these risks can create problems. The board of directors, management and shareholders should be able to make decisions based on a comprehensive analysis of financial risk. Managing risk with multiple factors is important because all the factors are interrelated and each affects the others, so the correlations between them must be analyzed. When viewing financial statements, one must consider the effects of inflation and interest rate changes, as well as exchange rate fluctuations. It is also important to analyze future events that may affect currency prices or interest rates that could affect balance sheets or income statements in different ways.

Question 8

Risk Functions

l VaR: Value at Risk, abbreviated as VaR, is defined as the worst loss expected from holding a security or portfolio over a given period of time, given a specified probability level (confidence level). For instance, assuming the VaR is $1 million at the one-month duration and with a 99% confidence level, this implies a 1% chance, under normal market movements, where the monthly loss exceeds $1 million.

VaR is therefore defined as: p= Pr[L> VaR]= 1= Fₐ(VaR), where the time period is a, L is the loss in value, p is the upper tail probability and Fₐ(x) the CDF of the loss. In R, VaR is computed as follows:

VaR(g, p=.95, method="historical")

Where g is the returns data and p represents a 95% confidence level.

The advantage of VaR is in the ease of understanding and its computation, hence its use as the de facto standard risk measure by regulators and financial institutions. Its also possible to compare and contrast the VaR’s of different portfolios and assets. However, VaR is uninformative of tail losses, as it only informs on what likely happens 95% of the time (if that is the confidence level), but informs nothing on what to expect should there be a loss in excess of VaR, that is 5% of the time. Another limitation is that VaR is not sub-additive, meaning combined risks are underestimated, consequently providing a loophole since firms could break themselves up to reduce their regulatory capital requirements as the sum of the smaller units would be less than that of the firm as a whole.

l Expected Tail Loss: The ETL, also known as the Expected Shortfall, is a risk measure that estimates the potential size of the loss exceeding VaR. It therefore gives attention to the tail of the risk distribution. It is therefore defined as:

ETL= E[L|L>VaR], where L is the loss function, and is computed in R as follows:

ES(g,p=0.95,method = "historical")

Where g is the returns data and p represents a 95% confidence level.

ETL is regarded a better risk measure than VaR since it informs on the worst-case scenario should the expected loss exceed the VaR. ETL is also a coherent risk measure, meaning it writes off the non-sub-additivity shortcoming of the VaR. However, ETL has its limitations as well, such as lower accuracy than VaR when dealing with losses that have fat tails (not normally distributed).

l Omega: The Omega ratio is the probability-weighted ratio of expected gains to expected losses given a specified threshold return target. The Omega ratio is non-parametric, meaning it makes no distributional assumption on returns. It takes into account all information in the historical returns’ distribution. It is defined as:

Ω=

where F(x) is the CDF of returns and r the desired threshold return. It can be computed in R as:

MAR = 0

print(OmegaSharpeRatio(g[,5], MAR))

where MAR is the Minimum Acceptable Return, set to 0 but adjustable, and g is the returns data.

The Omega Ratio is non-parametric, hence suitably captures returns that are highly asymmetric, that is returns exhibiting skewness and kurtosis, therefore the limitations brought about by distributional assumptions on returns are catered for. It therefore overrides the Sharpe Ratio which leans towards parametric distribution of returns.

l Drawdown: This is a measure of the duration taken by an asset or portfolio to recover its losses after falling from a historical peak. It is the peak-to-trough decline during a specific investment duration. Basically, drawdowns measure the downside volatility. A drawdown is successfully recorded once a new peak is recorded, as that indicates the end of that trough. In R, this can be computed as:

tS <- as.timeSeries(g)

head(tS)

drawdownPlot(g)

drawdowns(g)

Question 9

Coherence of Risk Functions

If the risk ratio satisfies consistency, monotonicity, good homogeneity, and structural consistency, it is considered consistent.

l Subadditivity: The structure states that the risks of the two positions cannot be worse than the sum of the risks involved in separating the portfolio, rather than the sum of the risks involved in separating the portfolio. Given two loss random variables L₁ and L₂, then p(L₁+ L₂)≤ p(L₁)+ p( L₂).

l Monotonicity: This property states than positions that always lead to higher losses require more risk capital, that is if L₁≤ L₂ then p(L₁)≤ p( L₂).

l Positive Homogeneity: This states that no diversification benefits are acquired by holding multiples of the same portfolio, L. In short, p(αL)= αp(L), α>0.

l Translational Invariance: The capital requirement is replaced once by adding or subtracting a fixed amount of from the area leading to the L loss; that is, p (L + ) = p (L) + p (L) + p (L) + p (L) + p (L) + p (L) + p (L) + p

The various coherence properties have different implications. For instance, a risk measure that violates the subadditivity property implies a loophole likely to be exploited by investors to avoid overstating the capital requirements, or rather to understate the total risk of the company by treating portfolios as separate entities rather than a wholesome entity. VaR has been shown to violate this property, making it an incoherent measure while ETL holds up to subadditivity hence coherent.

Question 10

Stock prices for 20 different companies will be used, and the data will be obtained from Yahoo Finance. The companies include; Microsoft Corporation, Apple Inc., Amazon, Advanced Micro Devices Inc., Ford Motor Company, NVIDIA Corporation, NIO Inc., Uber Technologies Inc., FTSE 100, US 3M , Nokia, etc.  This companies are selected since they contain the most active stocks. See the attached code.

 

Reference List

Engle, R. (2002). New frontiers for ARCH models. Journal of Applied Econometrics, 17(5), 425-446.

Geng, M. N. (2018). Fundamental drivers of house prices in advanced economies. International Monetary Fund.

Savva, C. S. (2018). Factors affecting housing prices: International evidence. Cyprus Economic Policy Review, 12(2), 87-96.

Tung, D. T., & Phung, V. T. H. (2019). An application of Altman z-score model to analyze the bankruptcy risk: Cases of multidisciplinary enterprises in Vietnam. Investment Management & Financial Innovations, 16(4), 181.

Zhang, X., Zhang, T., Young, A. A., & Li, X. (2014). Applications and comparisons of four time series models in epidemiological surveillance data. Plos one, 9(2), e88075.