What Factors do Influence the Nominal Risk-Free Rate (NRFR)?

An investor would be willing to forgo current consumption in order to increase future consumption at a rate of exchange called the risk-free rate of interest. This rate of exchange was measured in real terms because we assume that investors want to increase the consumption of actual goods and services rather than consuming the same amount that had come to cost more money. Therefore, when we discuss rates of interest, we need to differentiate between real rates of interest that adjust for changes in the general price level, as opposed to nominal rates of interest that are stated in money terms. That is, nominal rates of interest that prevail in the market are determined by real rates of interest, plus factors that will affect the nominal rate of interest, such as the expected rate of inflation and the monetary environment. It is important to understand these factors.

Notably, the variables that determine the RRFR change only gradually because we are concerned with long-run real growth. Therefore, you might expect the required rate on a risk-free investment to be quite stable over time. As discussed in connection with Exhibit 1.5, rates on three-month T-bills were not stable over the period from 2004 to 2010. This is demonstrated with additional observations in Exhibit 1.6, which contains yields on T-bills for the period 1987–2010.

Investors view T-bills as a prime example of a default-free investment because the government has unlimited ability to derive income from taxes or to create money from which to pay interest. Therefore, one could expect that rates on T-bills should change only gradually. In fact, the data in Exhibit 1.6 show a highly erratic pattern. Specifically, there was an increase in yields from 4.64 percent in 1999 to 5.82 percent in 2000 before declining by over 80 percent in three years to 1.01 percent in 2003, followed by an increase to 4.73 percent in 2006, and concluding at 0.14 percent in 2010. Clearly, the nominal rate of interest on a default-free investment is not stable in the long run or the short run, even though the underlying determinants of the RRFR are quite stable. As noted, two other factors influence the nominal risk-free rate (NRFR): (1) the relative ease or tightness in the capital markets, and (2) the expected rate of inflation.

Conditions in the Capital Market 

You will recall from prior courses in economics and finance that the purpose of capital markets is to bring together investors who want to invest savings with companies or governments who need capital to expand or to finance budget deficits. The cost of funds at any time (the interest rate) is the price that equates the current supply and demand for capital. Beyond this long-run equilibrium, change in the relative ease or tightness in the capital market is a short-run phenomenon caused by a temporary disequilibrium in the supply and demand of capital.

As an example, disequilibrium could be caused by an unexpected change in monetary policy (for example, a change in the target federal funds rate) or fiscal policy (for example, a change in the federal deficit). Such a change in monetary policy or fiscal policy will produce a change in the NRFR of interest, but the change should be short-lived because, in the longer run, the higher or lower interest rates will affect capital supply and demand. As an example, an increase in the federal deficit caused by an increase in government spending (easy fiscal policy) will increase the demand for capital and increase interest rates. In turn, this increase in interest rates should cause an increase in savings and a decrease in the demand for capital by corporations or individuals. These changes in market conditions should bring rates back to the long-run equilibrium, which is based on the long-run growth rate of the economy.

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What is The Real Risk-Free Rate?

The real risk-free rate (RRFR) is the basic interest rate, assuming no inflation and no uncertainty about future flows. An investor in an inflation-free economy who knew with certainty what cash flows he or she would receive at what time would demand the RRFR on an investment. Earlier, we called this the pure time value of money, because the only sacrifice the investor made was deferring the use of the money for a period of time. This RRFR of interest is the price charged for the risk-free exchange between current goods and future goods.

Two factors, one subjective and one objective, influence this exchange price. The subjective factor is the time preference of individuals for the consumption of income. When individuals give up $100 of consumption this year, how much consumption do they want a year from now to compensate for that sacrifice? The strength of the human desire for current consumption influences the rate of compensation required. Time preferences vary among individuals, and the market creates a composite rate that includes the preferences of all investors. This composite rate changes gradually over time because it is influenced by all the investors in the economy, whose changes in preferences may offset one another.

 

The objective factor that influences the RRFR is the set of investment opportunities available in the economy. The investment opportunities available are determined in turn by the long-run real growth rate of the economy. A rapidly growing economy produces more and better opportunities to invest funds and experience positive rates of return. A change in the economy’s long-run real growth rate causes a change in all investment opportunities and a change in the required rates of return on all investments. Just as investors supplying capital should demand a higher rate of return when growth is higher, those looking to borrow funds to invest should be willing and able to pay a higher rate of return to use the funds for investment because of the higher growth rate and better opportunities. Thus, a positive relationship exists between the real growth rate in the economy and the RRFR.

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How To Determine Required Rates Of Return?

Factors that you must consider when selecting securities for an investment portfolio. You will recall that this selection process involves finding securities that provide a rate of return that compensates you for: (1) the time value of money during the period of investment, (2) the expected rate of inflation during the period, and (3) the risk involved. 

The summation of these three components is called the required rate of return. This is the minimum rate of return that you should accept from an investment to compensate you for deferring consumption. Because of the importance of the required rate of return to the total investment selection process, this section contains a discussion of the three components and what influences each of them. 

The analysis and estimation of the required rate of return are complicated by the behavior of market rates over time. First, a wide range of rates is available for alternative investments at any time. Second, the rates of return on specific assets change dramatically over time. Third, the difference between the rates available (that is, the spread) on different assets changes over time.

The yield data in Exhibit 1.5 for alternative bonds demonstrate these three characteristics. First, even though all these securities have promised returns based upon bond contracts, the promised annual yields during any year differ substantially. As an example, during 2009 the average yields on alternative assets ranged from 0.15 percent on T-bills to 7.29 percent for Baa corporate bonds. Second, the changes in yields for a specific asset are shown by the three-month Treasury bill rate that went from 4.48 percent in 2007 to 0.15 percent in 2009. Third, an example of a change in the difference between yields over time (referred to as a spread) is shown by the Baa–Aaa spread. 4 The yield spread in 2007 was 91 basis points (6.47–5.56), but the spread in 2009 increased to 198 basis points (7.29–5.31). (A basis point is 0.01 percent.)

Because differences in yields result from the riskiness of each investment, you must understand the risk factors that affect the required rates of return and include them in your assessment of investment opportunities. Because the required returns on all investments change over time, and because large differences separate individual investments, you need to be aware of the several components that determine the required rate of return, starting with the risk-free rate.

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How To Measure Historical Returns?

To measure the risk for a series of historical rates of returns, we use the same measures as for expected returns (variance and standard deviation) except that we consider the historical holding period yields (HPYs) as follows:

The standard deviation is the square root of the variance. Both measures indicate how much the individual HPYs over time deviated from the expected value of the series. An example computation is contained in the appendix to this chapter. The standard deviation as a measure of risk (uncertainty) for the series or asset class is fairly common.

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How To Measure the Risk of Expected Rates of Return?

we can calculate the expected rate of return and evaluate the uncertainty, or risk, of an investment by identifying the range of possible returns from that investment and assigning each possible return a weight based on the probability that it will occur. Although the graphs help us visualize the dispersion of possible returns, most investors want to quantify this dispersion using statistical techniques. These statistical measures allow you to compare the return and risk measures for alternative investments directly. Two possible measures of risk (uncertainty) have received support in theoretical work on portfolio theory: the variance and the standard deviation of the estimated distribution of expected returns. In this section, we'll demonstrate how variance and standard deviation measure the dispersion of possible rates of return around the expected rate of return. The formula for variance is as follows:

Variance The larger the variance for an expected rate of return, the greater the dispersion of

expected returns and the greater the uncertainty, or risk, of the investment. The variance for

the perfect-certainty (risk-free) example would be:

Note that, in perfect certainty, there is no variance of return because there is no deviation from expectations and, therefore, no risk or uncertainty. The variance for the second example would be:

Standard Deviation 

The standard deviation is the square root of the variance:

For the second example, the standard deviation would be:

Therefore, when describing this investment example, you would contend that you expect a return of 7 percent, but the standard deviation of your expectations is 11.87 percent.

Relative Measure of Risk

In some cases, an unadjusted variance or standard deviation

can be misleading. If conditions for two or more investment alternatives are not similar—that is, if there are major differences in the expected rates of return—it is necessary to use a measure of relative variability to indicate risk per unit of expected return. A widely used relative measure of risk is the coefficient of variation (CV), calculated as follows:

The CV for the preceding example would be:

This measure of relative variability and risk is used by financial analysts to compare alternative investments with widely different rates of return and standard deviations of returns. As an illustration, consider the following two investments:

Comparing absolute measures of risk, investment B appears to be riskier because it has a standard deviation of 7 percent versus 5 percent for investment A. In contrast, the CV figures show that investment B has less relative variability or lower risk per unit of expected return because it has a substantially higher expected rate of return:

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How To Calculate Expected Rates of Return?

Risk is the uncertainty that an investment will earn its expected rate of return. An investor who is evaluating a future investment alternative expects or anticipates a certain rate of return. 

As an example, an investor may know that about 30 percent of the time the rate of return on this particular investment was 10 percent. Using this information along with future expectations regarding the economy, one can derive an estimate of what might happen in the future.

The expected return from an investment is defined as:

The investor might estimate probabilities for each of these economic scenarios based on past experience and the current outlook as follows:

The computation of the expected rate of return [E(Ri)] is as follows:

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How To Compute Arithmetic Mean & Geometric Mean

Single Investment Given a set of annual rates of return (HPYs) for an individual investment, there are two summary measures of return performance. The first is the arithmetic mean return, the second is the geometric mean return. To find the arithmetic mean (AM), the sum (Σ) of annual HPYs is divided by the number of years (n) as follows:

Where:

ΣHPY = the sum of annual holding period yields

An alternative computation, the geometric mean (GM), is the nth root of the product of the HPRs for n years minus one.

Where:

π = the product of the annual holding period returns as follows:

To illustrate these alternatives, consider an investment with the following data:

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How To Measure Holding Period Yield & Annual Holding Period Yield

Holding Period Return (HPR) to an annual percentage rate is to derive a percentage return, referred to as the holding period yield (HPY). The HPY is equal to the HPR minus 1.

To derive an annual HPY, you compute an annual HPR and subtract 1. Annual HPR is found by:

Assume an investment that cost $250 and is worth $350 after being held for two years:

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What Is Historical Rates of Return?

When we invest, we defer current consumption in order to add to our wealth so that we can consume more in the future. Therefore, when we talk about a return on an investment, we are concerned with the change in wealth resulting from this investment. This change in wealth can be either due to cash inflows, such as interest or dividends, or caused by a change in the price of the asset (positive or negative).

When you are evaluating alternative investments for inclusion in your portfolio, you will often be comparing investments with widely different prices or lives. As an example, you might want to compare a $15 stock that pays no dividends to a stock selling for $250 that pays dividends of $10 a year. To properly evaluate these two investments, you must accurately compare their historical rates of returns. A proper measurement of the rates of return is the purpose of this section.

If you commit $200 to an investment at the beginning of the year and you get back $220 at the end of the year, what is your return for the period? The period during which you own an investment is called its holding period, and the return for that period is the holding period return (HPR). In this example, the HPR is 1.10, calculated as follows:

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Definition Of Investment

Investment can be defined as the current commitment of dollars for a period of time in order to derive future payments that will compensate the investor for (i) the time the funds are committed, (ii) the expected rate of inflation during this time period, and (iii) the uncertainty of the future payments. The “investor” can be an individual, a government, a pension fund, or a corporation. Similarly, this definition includes all types of investments, including investments by corporations in plant and equipment and investments by individuals in stocks, bonds, commodities, or real estate. This text emphasizes investments by individual investors. In all cases, the investor is trading a known dollar amount today for some expected future stream of payments that will be greater than the current dollar amount today.

Hence, the question is why people invest and what they want from their investments. They invest to earn a return from savings due to their deferred consumption. They want a rate of return that compensates them for the time period of the investment, the expected rate of inflation, and the uncertainty of the future cash flows. This return, the investor’s required rate of return, is discussed throughout this book. A central question of this book is how investors select investments that will give them their required rates of return.

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Welcome To Finance School With Md Edrich Molla

Finance School With Md Edrich Molla, is one of the pioneer online site since many years. Hope you'll get lot of benefits from here. 

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Efficient Market Hypothesis (EMH) Meaning

An efficient capital market is one in which security prices adjust rapidly to the arrival of new information, and, therefore, the current prices of securities reflect all information about the security.

Fama divided the overall efficient market hypothesis (EMH) and the empirical tests of the hypothesis into three sub-hypotheses depending on the information set involved: (1) Weak-form EMH, (2) Semistrong-form EMH, and (3) Strong-form EMH.

 

# TYPES OF EMH

Weak-form of EMH

The weak-form EMH assumes that current stock prices fully reflect all security market information, including the historical sequence of prices, rates of return, trading volume data, and other market-generated information, such as odd-lot transactions and transactions by market makers. Because it assumes that current market prices already reflect all past returns and any other security market information, this hypothesis implies that past rates of return and other historical market data should have no relationship with future rates of return (that is, rates of return should be independent). Therefore, this hypothesis contends that you should gain little from using any trading rule which indicates that you should buy or sell a security based on past rates of return or any other past security market data.

 

Semistrong-form EMH

The semistrong-form EMH asserts that security prices adjust rapidly to the release of all public information; that is, current security prices fully reflect all public information. The semistrong hypothesis encompasses the weak-form hypothesis, because all the market information considered by the weak-form hypothesis, such as stock prices, rates of return, and trading volume, is public. Notably, public information also includes all nonmarket information, such as earnings and dividend announcements, price-to-earnings (P/E) ratios, dividend-yield (D/P) ratios, price-book value (P/BV) ratios, stock splits, news about the economy, and political news. This hypothesis implies that investors who base their decisions on any important new information after it is public should not derive above-average risk-adjusted profits from their transactions, considering the cost of trading because the security price should immediately reflect all such new public information.

 

Strong-form EMH

The strong-form EMH contends that stock prices fully reflect all information from public and private sources. This means that no group of investors has monopolistic access to information relevant to the formation of prices. Therefore, this hypothesis contends that no group of investors should be able to consistently derive above-average risk-adjusted rates of return. The strong-form EMH encompasses both the weak-form and the semistrong-form EMH. Further, the strong-form EMH extends the assumption of efficient markets, in which prices adjust rapidly to the release of new public information, to assume perfect markets, in which all information is cost-free and available to everyone at the same time.

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What Is Beta?

Beta (β) is a Greek alphabet used in finance to denote the volatility or systematic risk of a security or portfolio compared to the market.

# HOW BETA WORKS

A beta coefficient shows the volatility of an individual stock compared to the systematic risk of the entire market. Beta represents the slope of the line through a regression of data points. In finance, each point represents an individual stock's returns against the market.

Beta effectively describes the activity of a security's returns as it responds to swings in the market. It is used in the capital asset pricing model (CAPM), which describes the relationship between systematic risk and expected return for assets. CAPM is used to price risky securities and to estimate the expected returns of assets, considering the risk of those assets and the cost of capital.

# HOW TO CALCULATE BETA?

A security's beta is calculated by dividing the product of the covariance of the security's returns and the market's returns by the variance of the market's returns over a specified period. The calculation helps investors understand whether a stock moves in the same direction as the rest of the market. It also provides insights into how volatile–or how risky–a stock is relative to the rest of the market.

# WHAT ARE THE BETA VALUES?

Beta Equal to 1; A stock with a beta of 1.0 means its price activity correlates with the market. Adding a stock to a portfolio with a beta of 1.0 doesn’t add any risk to the portfolio, but doesn’t increase the likelihood that the portfolio will provide an excess return.

Beta Less than 1; A beta value less than 1.0 means the security is less volatile than the market. Including this stock in a portfolio makes it less risky than the same portfolio without the stock. Utility stocks often have low betas because they move more slowly than market averages.

Beta Greater than 1; A beta greater than 1.0 indicates that the security's price is theoretically more volatile than the market. If a stock's beta is 1.2, it is assumed to be 20% more volatile than the market. Technology stocks tend to have higher betas than the market benchmark. Adding the stock to a portfolio will increase the portfolio’s risk, but may also increase its return.

Negative Beta; A beta of -1.0 means that the stock is inversely correlated to the market benchmark on a 1:1 basis. Put options and inverse ETFs are designed to have negative betas. There are also a few industry groups, like gold miners, where a negative beta is common.

Investors commonly evaluate two categories of risk. Systematic risk is the risk of the entire market declining, called un-diversifiable. Unsystematic, or diversifiable risk, is the uncertainty associated with an individual stock or industry. It is risk related to a company or sector and can be mitigated through diversification.

# IS BETA A GOOD MEASURE OF RISK?

Beta can provide some risk information, but it is not an effective measure of risk. Beta only looks at a stock's past performance relative to the S&P 500 and does not predict future moves. It also does not consider the fundamentals of a company or its earnings and growth potential.

# HOW DO INVESTORS INTERPRET A STOCK'S BETA?

A Beta of 1.0 for a stock means it has been as volatile as the broader market. If the index moves up or down 1%, so too would the stock, on average. Betas larger than 1.0 indicate greater volatility - so if the beta were 1.5 and the index moved up or down 1%, the stock would have moved 1.5%, on average. Betas less than 1.0 indicate less volatility: if the stock had a beta of 0.5, it would have risen or fallen just half a percent as the index moved 1%.

# IS BETA A HELPFUL MEASURE FOR LONG TERM INVESTMENTS?

While beta can offer useful information when evaluating a stock, it does have some limitations. Beta can determine a security's short-term risk and analyze volatility. However, beta is calculated using historical data points and is less meaningful for investors looking to predict a stock's future movements for long-term investments. A stock's volatility can change significantly over time, depending on a company's growth stage and other factors. 

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Definition Of Alpha

Alpha (α) is popularly used in investing to explain an investment strategy’s ability to gain high level of profit. Alpha is therefore also generally known as excess return or the abnormal rate of return comparing to a benchmark, when adjusted for risk.

We also can say, alpha is the excess return on an investment that is not a result of a general movement of the security market. Hence, a zero alpha would indicate that the portfolio or fund is going perfectly with the benchmark index and that the manager has not added or lost any additional value in the market.

# APPLICATION OF ALPHA IN INVESTMENT

Alpha is used in finance as a measure of performance, indicating when a strategy, trader, or portfolio manager has managed to beat the market return or other benchmark over some period. Alpha, often considered the active return on an investment, gauges the performance of an investment against a market index or benchmark that is considered to represent the market’s movement as a whole.

The excess return of an investment relative to the return of a benchmark index is the investment’s alpha. Alpha may be positive or negative and is the result of active investing. Beta, on the other hand, can be earned through passive index investing.

Active portfolio managers seek to generate alpha in diversified portfolios, with diversification intended to eliminate unsystematic risk. Because alpha represents the performance of a portfolio relative to a benchmark, it is often considered to represent the value that a portfolio manager adds to or subtracts from a fund’s return.

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Definition Of Behavioral Finance

 Behavioral finance can be defined as the study of investors’ psychology that impacts while making investment decision in the securities markets. It focuses on different psychological biases such as overconfidence, loss aversion, confirmation, anchoring and so on which directly impact investors’ decision making process on a particular security’s buying or selling.

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Definition Of Economics

In earth resources are limited but wants and demands are unlimited. It causes a lot of problems for the people around the globe to fulfill their sky-limit desires. Economics, the concept comes to us to clarify how to manage unlimited wants and demand by the limited resources.

Therefore, economics precisely can be defined as the studies of managing limitless needs, wants and demands by the limited assets or resources. It explains what to produce, how to produce, for whom to produce.   

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