Assignment 8513 (Q NO.5)

Q. 5      

Explain Modern Portfolio Theory (MPT). Discuss types of risk highlighted by MPT with Example.                                                                              

Ans

Modern Portfolio Theory (MPT)

Modern Portfolio Theory (MPT), a hypothesis put forth by Harry Markowitz in his paper "Portfolio Selection," (published in 1952 by the Journal of Finance) is an investment theory based on the idea that risk-averse investors can construct portfolios to optimize or maximize expected return based on a given level of market risk, emphasizing that risk is an inherent part of higher reward. It is one of the most important and influential economic theories dealing with finance and investment.

Also called "portfolio theory" or "portfolio management theory," MPT suggests that it is possible to construct an "efficient frontier" of optimal portfolios, offering the maximum possible expected return for a given level of risk. It suggests that it is not enough to look at the expected risk and return of one particular stock. By investing in more than one stock, an investor can reap the benefits of diversification, particularly a reduction in the riskiness of the portfolio. MPT quantifies the benefits of diversification, also known as not putting all of your eggs in one basket.

Consider that, for most investors, the risk they take when they buy a stock is that the return will be lower than expected. In other words, it is the deviation from the average return. Each stock has its own standard deviation from the mean, which MPT calls "risk."

The risk in a portfolio of diverse individual stocks will be less than the risk inherent in holding any one of the individual stocks (provided the risks of the various stocks are not directly related). Consider a portfolio that holds two risky stocks: one that pays off when it rains and another that pays off when it doesn't rain. A portfolio that contains both assets will always pay off, regardless of whether it rains or shines. Adding one risky asset to another can reduce the overall risk of an all-weather portfolio. 

In other words, Markowitz showed that investment is not just about picking stocks, but about choosing the right combination of stocks among which to distribute one's nest egg.

On the more technical side, there are five statistical risk measurements used in modern portfolio theory (MPT); alpha, beta, standard deviation, R-squared and the Sharpe ratio. All of these indicators are intended to help investors determine a potential investment's risk-reward profile.

MPT makes the assumption that investors are risk-averse, meaning they prefer a less risky portfolio to a riskier one for a given level of return. This implies than an investor will take on more risk only if he or she is expecting more reward.

The expected return of the portfolio is calculated as a weighted sum of the individual assets' returns. If a portfolio contained four equally-weighted assets with expected returns of 4, 6, 10 and 14%, the portfolio's expected return would be:

(4% x 25%) + (6% x 25%) + (10% x 25%) + (14% x 25%) = 8.5%

The portfolio's risk is a complicated function of the variances of each asset and the correlations of each pair of assets. To calculate the risk of a four-asset portfolio, an investor needs each of the four assets' variances and six correlation values, since there are six possible two-asset combinations with four assets. Because of the asset correlations, the total portfolio risk, or standard deviation, is lower than what would be calculated by a weighted sum.

Types of risk highlighted by MPT with Example

Modern Portfolio Theory focuses on the effect investments have on an entire portfolio, rather than as a single investment. In other words, choosing different types of investments will diversify your risk.

Markowitz wanted to prove that looking at investments as a whole portfolio rather than individual investments will provide greater returns in the end.

 Example

You invest in three stocks individually, not focusing on how they affect your entire portfolio. This means you are at the mercy of the stock market alone. If stocks in general drop, you could face serious risk without anything to offset that risk.

But if instead, you diversify without putting all of your eggs in one basket, you may offset your risk.

Let's say that instead of investing in just stocks, you put some money in bonds too. The bonds may offset the riskiness of the stocks. If stock prices drop, the bond prices may increase, helping to decrease the risk of a complete loss.

This is a simplified example. But it shows you how choosing a variety of investments from different asset classes can offset your risk.

Modern Portfolio Theory assumes that investors see risk and return as directly related we need to take a higher risk in order to receive higher returns.

The theory suggests, though, that diversifying will reduce the risk without reducing your returns. In other words, an investor should choose the portfolio with the lower risk without sacrificing the return.

Assignment 8513 (Q NO.4)

Q. 4

Discuss the following:                                                         (20)

1.   Technical Analysis

2.   Fundamental Analysis

3.   Horizontal Analysis

4.   Vertical Analysis

Ans part 1

Technical Analysis

Technical analysis is a trading discipline employed to evaluate investments and identify trading opportunities by analyzing statistical trends gathered from trading activity, such as price movement and volume. Unlike fundamental analysts, who attempt to evaluate a security's intrinsic value, technical analysts focus on patterns of price movements, trading signals and various other analytical charting tools to evaluate a security's strength or weakness.

Technical analysis can be used on any security with historical trading data. This includes stocks, futures, commodities, fixed-income, currencies, and other securities. In this tutorial, we’ll usually analyze stocks in our examples, but keep in mind that these concepts can be applied to any type of security. In fact, technical analysis is far more prevalent in commodities and forex markets where traders focus on short-term price movements.

Technical analysts believe past trading activity and price changes of a security can be valuable indicators of the security's future price movements. They may use technical analysis independent of other research efforts or in combination with some concepts of intrinsic value considerations but most often their convictions are based solely on the statistical charts of a security. The Market Technicians Association (MTA) is one of the most popular groups supporting technical analysts in their investments with the Chartered Market Technicians (CMT) designation a popular certification for many advanced technical analysts.

There are two primary methods used to analyze securities and make investment decisions: fundamental analysis and technical analysis. Fundamental analysis involves analyzing a company’s financial statements to determine the fair value of the business, while technical analysis assumes that a security’s price already reflects all publicly-available information and instead focuses on the statistical analysis of price movements. Technical analysis attempts to understand the market sentiment behind price trends by looking for patterns and trends rather than analyzing a security’s fundamental attributes.

Charles Dow released a series of editorials discussing technical analysis theory. His writings included two basic assumptions that have continued to form the framework for technical analysis trading.

1. Markets are efficient with values representing factors that influence a security’s price, but
2. Market price movements are not purely random but move in identifiable patterns and trends that tend to repeat over time

Ans part 2

Fundamental analysis

Fundamental analysis is a method of evaluating a security in an attempt to assess its intrinsic value, by examining related economic, financial, and other qualitative and quantitative factors. Fundamental analysts study anything that can affect the security's value, including macroeconomic factors (e.g. economy and industry conditions) and microeconomic factors (e.g. financial conditions and company management). The end goal of fundamental analysis is to produce a quantitative value that an investor can compare with a security's current price, thus indicating whether the security is undervalued or overvalued.

Fundamental analysis determines the health and performance of an underlying company by looking at key numbers and economic indicators. The purpose is to identify fundamentally strong companies or industries and fundamentally weak companies or industries. Investors go long (purchasing with the expectation that the stock will rise in value) on the companies that are strong, and short (selling shares that you believe will drop in value with the expectation of repurchasing when at a lower price) the companies that are weak. This method of security analysis is considered to be the opposite of technical analysis, which forecasts the direction of prices through the analysis of historical market data, such as price and volume.

Fundamental analysis uses real, public data in the evaluation a security's value. Although most analysts use fundamental analysis to value stocks, this method of valuation can be used for just about any type of security. For example, an investor can perform fundamental analysis on a bond's value by looking at economic factors, such as interest rates and the overall state of the economy. He can also look at information about the bond issuer, such as potential changes in credit ratings.

For stocks and equity instruments, fundamental analysis uses revenues, earnings, future growth, return on equity, profit margins, and other data to determine a company's underlying value and potential for future growth. In terms of stocks, fundamental analysis focuses on the financial statements of the company being evaluated. One of the most famous and successful fundamental analysts is the so-called "Oracle of Omaha," Warren Buffett, who is well known for successfully employing fundamental analysis to pick securities.

 Example of Fundamental Analysis

Even the market as a whole can be evaluated using fundamental analysis. For example, analysts looked at fundamental indicators of the S&P 500 from July 4 to July 8, 2016. During this time, the S&P rose to 2129.90 after the release of a positive jobs' report in the United States. In fact, the market just missed a new record high, coming in just under the May 2015 high of 2132.80. The economic surprise of an additional 287,000 jobs for the month of June specifically increased the value of the stock market on July 8, 2016.

However, there are differing views on the market's true value. Some analysts believe the economy is heading for a bear market, while other analysts believe it will continue as a bull market.

Ans part 3

Horizontal Analysis

Horizontal analysis is used in financial statement analysis to compare historical data, such as ratios, or line items, over a number of accounting periods. Horizontal analysis can either use absolute comparisons or percentage comparisons, where the numbers in each succeeding period are expressed as a percentage of the amount in the baseline year, with the baseline amount being listed as 100%. This is also known as base-year analysis.

Horizontal analysis allows investors and analysts to see what has been driving a company's financial performance over a number of years, as well as spotting trends and growth patterns such as seasonality. It enables analysts to assess relative changes in different line items over time, and project them. By looking at the income statement, balance sheet and cash flow statement at the same time, one can create a complete picture of operational results, and see what has been driving a company’s performance and whether it is operating efficiently and profitably.

The analysis of critical measures of business performance, such as profit margins, inventory turnover and return on equity, can detect emerging problems and strengths. For example, earnings per share (EPS) may have been rising because the cost of goods sold has been falling, or because sales have been growing strongly. And coverage ratios, like the cash flow-to-debt ratio and the interest coverage ratio can reveal whether a company can service its debt and has enough liquidity. Horizontal analysis also makes it easier to compare growth rates and profitability among different companies.

Horizontal Analysis Example

Horizontal analysis typically shows the changes from the base period in dollar and percentage. For example, when someone says that revenues have increased by 10% this past quarter, that person is using horizontal analysis. The percentage change is calculated by first dividing the dollar change between the comparison year and the base year by the item value in the base year, then multiplying the quotient by 100%.

For example, assume an investor wishes to invest in company XYZ. The investor may wish to determine how the company grew over the past year. Assume that in company XYZ's base year, it reported net income of $10 million and retained earnings of $50 million. In the current year, company XYZ reported net income of $20 million and retained earnings of $52 million. Consequently, it has an increase of $10 million in its net income and $2 million in its retained earnings year over year. Therefore, company ABC's net income grew by 100% YOY, while its retained earnings only grew by 4%.

Ans part 4

Vertical analysis

Vertical analysis is a method of financial statement analysis in which each line item is listed as a percentage of a base figure within the statement. Thus, line items on an income statement can be stated as a percentage of gross sales, while line items on a balance sheet can be stated as a percentage of total assets or liabilities, and vertical analysis of a cash flow statement shows each cash inflow or outflow as a percentage of the total cash inflows.

Vertical analysis makes it much easier to compare the financial statements of one company with another, and across industries because one can see the relative proportions of account balances. It also makes it easier to compare previous periods for time series analysis, in which quarterly and annual figures are compared over a number of years in order to gain a picture of whether performance metrics are improving or deteriorating.

For example, by showing the various expense line items in the income statement as a percentage of sales, one can see how these are contributing to profit margins and whether profitability is improving over time. It also makes it easier to compare the profitability of a company with its peers.

Financial statements that include vertical analysis clearly show line item percentages in a separate column. These types of financial statements, including detailed vertical analysis, are also known as common-size financial statements and are used by many companies to provide greater detail on a company’s financial position. Common-size financial statements often incorporate comparative financial statements that include columns comparing each line item to a previously reported period.

Assignment 8513 (Q NO.3)

Q.3

Discuss the following:                                                         (20)

1.       Time Value of Money

2.       Compounding

3.       Discounting

4.       Annuities

5.       Perpetuities

Ans part 1                       

Time Value of Money

The time value of money (TVM) is the concept that money available at the present time is worth more than the identical sum in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also sometimes referred to as present discounted value.

The time value of money draws from the idea that rational investors prefer to receive money today rather than the same amount of money in the future because of money's potential to grow in value over a given period of time. For example, money deposited into a savings account earns a certain interest rate, and is therefore said to be compounding in value. 

Further illustrating the rational investor's preference, assume you have the option to choose between receiving $10,000 now versus $10,000 in two years. It's reasonable to assume most people would choose the first option. Despite the equal value at time of disbursement, receiving the $10,000 today has more value and utility to the beneficiary than receiving it in the future due to the opportunity costs associated with the wait. Such opportunity costs could include the potential gain on interest were that money received today and held in a savings account for two years.

Depending on the exact situation in question, the TVM formula may change slightly. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or less factors. But in general, the most fundamental TVM formula takes into account the following variables:

• FV = Future value of money
• PV = Present value of money
• i = interest rate
• n = number of compounding periods per year
• t = number of years

Based on these variables, the formula for TVM is:

FV = PV x [ 1 + (i / n) ] ^{(n x t)}

Assume a sum of $10,000 is invested for one year at 10% interest. The future value of that money is:

FV = $10,000 x (1 + (10% / 1) ^ (1 x 1) = $11,000

The formula can also be rearranged to find the value of the future sum in present day dollars. For example, the value of $5,000 one year from today, compounded at 7% interest, is:

PV = $5,000 / (1 + (7% / 1) ^ (1 x 1) = $4,673

Ans part 2

Compounding

Compounding is the process in which an asset's earnings, from either capital gains or interest, are reinvested to generate additional earnings over time. This growth, calculated using exponential functions, occurs because the investment will generate earnings from both its initial principal and the accumulated earnings from preceding periods. Compounding, therefore, differs from linear growth, where only the principal earns interest each period.

Compounding typically refers to the increasing value of an asset due to the interest earned on both a principal and accumulated interest. This phenomenon, which is a direct realization of the time value of money (TMV) concept, is also known as compound interest. Compound interest works on both assets and liabilities. While compounding boosts the value of an asset more rapidly, it can also increase the amount of money owed on a loan, as interest accumulates on the unpaid principal and previous interest charges.

To illustrate how compounding works, suppose $10,000 is held in an account that pays 5% interest annually. After the first year, or compounding period, the total in the account has risen to $10,500, a simple reflection of $500 in interest being added to the $10,000 principal. In year two, the account realizes 5% growth on both the original principal and the $500 of first-year interest, resulting in a second-year gain of $525 and a balance of $11,025. After 10 years, assuming no withdrawals and a steady 5% interest rate, the account would grow to $16,288.95.

The formula for the future value (FV) of a current asset relies on the concept of compound interest. It takes into account the present value of an asset, the annual interest rate, and the frequency of compounding (or number of compounding periods) per year and the total number of years. The generalized formula for compound interest is:

FV = PV x [1 + (i / n)] ^{(n x t)}, where:

• FV = future value
• PV = present value
• i = the annual interest rate
• n = the number of compounding periods per year
• t = the number of years

Example

The effects of compounding strengthen as the frequency of compounding increases. Assume a one-year time period. The more compounding periods throughout this one year, the higher the future value of the investment, so naturally, two compounding periods per year are better than one, and four compounding periods per year are better than two.

To illustrate this effect, consider the following example given the above formula. Assume that an investment of $1 million earns 20% per year. The resulting future value, based on a varying number of compounding periods, is:

• Annual compounding (n = 1): FV = $1,000,000 x [1 + (20%/1)] ^{(1 x 1)} = $1,200,000
• Semi-annual compounding (n = 2): FV = $1,000,000 x [1 + (20%/2)] ^{(2 x 1)} = $1,210,000
• Quarterly compounding (n = 4): FV = $1,000,000 x [1 + (20%/4)] ^{(4 x 1)} = $1,215,506
• Monthly compounding (n = 12): FV = $1,000,000 x [1 + (20%/12)] ^{(12 x 1)} = $1,219,391
• Weekly compounding (n = 52): FV = $1,000,000 x [1 + (20%/52)] ^{(52 x 1)} = $1,220,934
• Daily compounding (n = 365): FV = $1,000,000 x [1 + (20%/365)] ^{(365 x 1)} = $1,221,336

As evident, the future value increases by a smaller margin even as the number of compounding periods per year increases significantly. The frequency of compounding over a set length of time has a limited effect on an investment's growth. This limit, based on calculus, is known as continuous compounding and can be calculated using the formula:

FV = PV x e ^{(i x t)}, where e = the irrational number 2.7183.

In the above example, the future value with continuous compounding equals: FV = $1,000,000 x 2.7183 ^{(0.2 x 1)} = $1,221,403.

Ans part 3

Discounting

Discounting is the process of determining the present value of a payment or a stream of payments that is to be received in the future. Given the time value of money, a dollar is worth more today than it would be worth tomorrow. Discounting is the primary factor used in pricing a stream of tomorrow's cash flows.

For example, the coupon payments found in a regular bond are discounted by a certain interest rate and added together with the discounted par value to determine the bond's current value.

From a business perspective, an asset has no value unless it can produce cash flows in the future. Stocks pay dividends. Bonds pay interest, and projects provide investors with incremental future cash flows. The value of those future cash flows in today's terms is calculated by applying a discount factor to future cash flows.

In general, a higher the discount means that there is a greater the level of risk associated with an investment and its future cash flows. For example, the cash flows of company earnings are discounted back at the cost of capital in the discounted cash flows model. In other words, future cash flows are discounted back at a rate equal to the cost of obtaining the funds required to finance the cash flows. A higher interest rate paid on debt also equates with a higher level of risk, which generates a higher discount and lowers the present value of the bond. Indeed, junk bonds are sold at a deep discount. Likewise, a higher the level of risk associated with a particular stock, represented as beta in the capital asset pricing model, means a higher discount, which lowers the present value of the stock.

Ans part 4

Annuities

An annuity is a series of equal payments made at equal intervals during a period of time. In other words, it’s a system of making or receiving payments where the payment amount and time period between payments is equal.

Example

Many people play the lottery in hopes to cash in on the big jackpot. Unfortunately, most people don’t win it big, but an extremely small percentage of people do. After they win, they often have to make the choice whether to be paid in a lump sum or in an annuity. For example, a million dollar jackpot could be paid out immediately in one lump sum of $600,000 or in $5,000 monthly installments for 15 years.

This option takes the time value of money into consideration. Notice that neither option actually pays out a full $1,000,000. This is because over time money should earn interest. Thus, $600,000 today will equal $1,000,000 in the future after interest is added up over the years. The same is true for the annuity payments.

Loans are also set up as annuities. Sometimes people don’t think of them as annuities because they are not receiving the payments. Remember annuities are just agreements with equal payments and time intervals. When a business signs a loan with a bank, it agrees to make a payment each month for specific amount. The payments are due each month until the loan principle is paid off.

In present value calculations, an annuity is a series of equal cash amounts occurring at equal time intervals. The identical cash amounts are sometimes referred to as payments, receipts, or rent.

Some examples of business transactions that form an annuity include:

1.   The equal amounts of interest paid every six months by the issuer of debt securities known as bonds.

2.   The monthly payments required by a lease agreement for equipment or a vehicle.

3.   The annual payments required by a purchase agreement.

The annuity payments are often discounted to arrive at their present value. The annuity payments can also be used to determine the effective interest rate that is embedded in an agreement.

Depending on the starting point of the first payment, an annuity will be further identified as an ordinary annuity, an annuity in advance, a deferred annuity, etc.

Ans part 5

Perpetuities

Perpetuity in the financial system is a situation where a stream of cash flow payments continues indefinitely or is an annuity which has no end. In valuation analysis, perpetuities are used to find the present value of a company’s future projected cash flow stream and company’s terminal value. Essentially, perpetuity is a series of cash flows that keep paying out forever.

Perpetuity refers to an infinite amount of time. In finance, perpetuity is a constant stream of identical cash flows with no end. The present value of a security with perpetual cash flows can be determined as:

The concept of a perpetuity is also used in a number of financial theories, such as in the dividend discount model (DDM).

An annuity is a stream of cash flows. Perpetuity is a type of annuity that lasts forever, into perpetuity. The stream of cash flows continues for an infinite amount of time. In finance, a person uses the perpetuity calculation in valuation methodologies to find the present value of a company's cash flows when discounted back at a certain rate. An example of a financial instrument with perpetual cash flows is the the British-issued bonds known as consols. By purchasing a consol from the British government, the bondholder is entitled to receive annual interest payments forever. Although it may seem a bit illogical, an infinite series of cash flows can have a finite present value. Because of the time value of money, each payment is only a fraction of the last.

Specifically, the perpetuity formula determines the amount of cash flows in the terminal year of operation. In valuation, a company is said to be a going concern, meaning that it goes on forever. For this reason, the terminal year is perpetuity, and analysts use the perpetuity formula to find its value.

Example

For example, if a company is projected to make $100,000 in year 10, and the company’s cost of capital is 8%, with a long-term growth rate of 3%, the value of the perpetuity is:

= [Cash Flow_{Year 10} x (1 + g)] / (r - g)

= ($100,000 x 1.03) / (0.08 - 0.03)

= $103,000 / 0.05

= $2.06 million

This means that $100,000 paid into a perpetuity, assuming a 3% rate of growth with an 8% cost of capital, is worth $2.06 million in 10 years. Now, a person must find the value of that $2.06 million today. To do this, analysts use another formula referred to as the present value of a perpetuity.