Logic for the 2 statements:

1. N-spread doesn’t consider term structure of spot rate. It simply assume benchmark spot rate curve is flat. That’s why it is only a one-point (last point) spread. Z-spread cures this problem; it measures spread along every point of the spot curve. So if the spot curve in flat, Z-spread = N spread; on the other hand, the steeper the curve, the greater of differene of them.  What is important to note is The zero-volatility spread (or Z-spread, or static spread) is a measure of the spread that the investor would realize over the entire Treasury spot rate curve if the bond is held to maturity, thereby recognizing the term structure of interest rates. Unlike the nominal spread, the Z-spread is not a spread off one point on the Treasury yield curve but a spread over the entire spot rate curve. It represents a spread to compensate for the target bond’s added risks including credit risk, liquidity risk and volatility risk associated with embedded options.

2. N spread doesn’t consider cash flow change. Earlier principal payback definitely change cash flow. Z spread would adress this change. So compared to stable cash flow bond (bullet maturity bond), armortized bond has Z-spread which is different from N-spread.  For bullet bonds, unless the yield curve is very steep, the nominal spread will not differ significantly from the Z-spread; for securities where principal is repaid over time rather than just at maturity there can be a significant difference, particularly in a steep yield curve environment.

Mike Weishot wants to purchase the Sysco bond shown below. Its rating has declined to BBB+, has a coupon of 11.40% and a price of 117.436. Mike is concerned about both the nominal spread and the Z spread and calculates both carefully. The comparable maturity Treasury has a YTM of 5% and the Sysco bond is currently providing bondholders a YTM of 5.822%. Given the Treasury data below and the information provided above, what is the difference between the zero-volatility spread and the nominal spread

In order to calculate the Risk Premium, one needs to use the correct Risk Free Rate.  In theory, the risk-free rate is the minimum return an investor should expect for any investment, as any amount of risk would not be tolerated unless the expected rate of return was greater than the risk-free rate. In practice, however, the risk-free rate does not technically exist; even the safest investments carry a very small amount of risk.

Most financial analysts use the US Treasury rates as a proxy to the Risk Free Rate. The risk free rate you use should be consistent with the time horizon of the investment. Typically the yield on the 10-year note is used for stocks. To be more accurate its better to use STRIPS or zero coupon bonds to avoid the effect of reinvestment of the coupons.

a- at lower wage rates than at higher

b- in the long run than in the short

c- the less labor intenssive the process.

Elasticity of labor must also be looked at in terms of the substitutability with capital, the other factor of production. When the wage is low, a lot of labor has been employed. Thus, if the wage rate rises then the labor can be fired to hire more capital. You shouldn’t be thinking in terms of the demand curve because that only shows the relationship between price and quantity demanded.

Think about an isoquant (set of points at which the same quantity of output is produced while changing the quantities of two or more inputs), where you have the two factors of production on the two axes. Towards each end of the isoquant, you’re employing a lot of one factor and very little of the other, so it’s hard to switch away from the factor you’re not using much from. Not sure if that makes a lot of sense, but that’s what they’re getting at in this question.

a- An economically efficient process must be technologically efficient also

b- An economically efficient process is not necessarily technologically efficient

c- A production process cannot be technologically efficient unless it is economically efficient

The answer to the above question is: A.

There are two concepts of efficiency: Technological efficiency occurs when it is not possible to increase output without increasing inputs. Economic efficiency occurs when the cost of producing a given output is as low as possible. Technological efficiency is an engineering matter. Given what is technologically feasible, something can or cannot be done. Economic efficiency depends on the prices of the factors of production. Something that is technologically efficient may not be economically efficient. But something that is economically efficient is always technologically efficient. A key point to understand is the idea that economic efficiency occurs “when the cost of producing a given output is as low as possible”. There’s a hidden assumption here, and that is the assumption that all else being equal. A change that lowers the quality of the good while at the same time lowers the cost of production does not increase economic efficiency. The concept of economic efficiency is only relevant when the quality of goods being produced is unchanged.

In other words, if on 1st September the Spot Price > Forward Price for the contract expiring on the 30th September (which is called backwardation). As the contract approaches maturity, the forward price approaches the spot price. On 30th September, a new contract which expires on 30th October would be again trading at  below the current spot (if the market is still in backwardation). Thus, the old contract which expires on the 30th September can be sold for a higher price, and the new contract can be bought at a lower price. By selling the old at a higher price and buying the new at a lower price, a return is generated. This is called roll yield.

E.g. Spot price Rs.50, Future price Rs.48 (for one month later) and Future price (of a contract 2 months later) is Rs.45. Now if the spot price does not change for the first month and you had bought the first future at 48, as the month passes, this future price of the first month will converge to Rs.50. So you would be able to book your profits of Rs.2 on the contract. But if you wish to maintain exposure of the commodity, you can buy next month contract which if again is trading in backwardation would be priced at Rs. 47 for example. You can sell the future for 50 and then buy the next month contract which was earlier on 45 and assuming has moved to 47. This way you can roll over contract into cheaper rates.

Roll Yield is, therefore, positive for the Long Position in Backwardation and Negative in Contango.

Note: For the short position the roll yield would be negative in Backwardation and positive in Contango.

Money Multiplier: The expansion of a country’s money supply that results from banks being able to lend. The size of the multiplier effect depends on the percentage of deposits that banks are required to hold as reserves. In other words, it is money used to create more money and is calculated by dividing total bank deposits by the reserve requirement. The multiplier effect depends on the set reserve requirement. So, to calculate the impact of the multiplier effect on the money supply, we start with the amount banks initially take in through deposits and divide this by the reserve ratio. If, for example, the reserve requirement is 20%, for every $100 a customer deposits into a bank, $20 must be kept in reserve. However, the remaining $80 can be loaned out to other bank customers. This $80 is then deposited by these customers into another bank, which in turn must also keep 20%, or $16, in reserve but can lend out the remaining $64. This cycle continues – as more people deposit money and more banks continue lending it – until finally the $100 initially deposited creates a total of $500 ($100 / 0.2) in deposits. This creation of deposits is the multiplier effect. The higher the reserve requirement, the tighter the money supply, which results in a lower multiplier effect for every dollar deposited. The lower the reserve requirement, the larger the money supply, which means more money is being created for every dollar deposited.

Rent seeking occurs when an individual, organization or firm seeks to earn income by capturing economic rent through manipulation or exploitation of the economic or political environment, rather than by earning profits through economic transactions and the production of added wealth. While there may be few people in modern industrialized countries who do not gain something, directly or indirectly, through some form or another of rent seeking, rent seeking in the aggregate can impose substantial losses on society. Rent seeking can be performed by either buying a monopoly or by creating a monopoly.
Hence, the firm’s rent seeking costs are treated as fixed costs, which get added to the total fixed costs and to the average total cost. The ATC curve shifts upward until, at the profit maximisation price, the firm breaks even. This means that a firm which is a rent seeker only makes a normal profit.

Monte Carlo Simulation: A problem solving technique used to approximate the probability of certain outcomes by running multiple trial runs, called simulations, using random variables. Monte Carlo simulation is a computerized mathematical technique that allows people to account for risk in quantitative analysis and decision making. The technique is used by professionals in such widely disparate fields as finance, project management, energy, manufacturing, engineering, research and development, insurance, oil & gas, transportation, and the environment. Monte Carlo simulation furnishes the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action.. It shows the extreme possibilities—the outcomes of going for broke and for the most conservative decision—along with all possible consequences for middle-of-the-road decisions.

It is important to note the following points:

• The larger variance should always be placed in the numerator
• The test statistic is F = s1^2 / s2^2 where s1^2 > s2^2
• Divide alpha by 2 for a two tail test and then find the right critical value i.e. even if the hypothesis is stated as a 2 tailed, there is only one critical value.
• If standard deviations are given instead of variances, they must be squared
• When the degrees of freedom aren’t given in the table, go with the value with the larger critical value (this happens to be the smaller degrees of freedom). This is so that you are less likely to reject in error (type I error)
• The populations from which the samples were obtained must be normal.
• The samples must be independent
• The test statistic has two degrees of freedom (n1 – 1) for the numerator and (n2 – 1) for the denominator

The basis of the approach is that the company has two main sources of risk: a) the risk that is inherent in the business (operating risk) and b) the risk due to leverage of the financial structure. Now the point is, the the first risk which is operational in nature is comparable among companies in the same industry, whereas the financial risk is more of a management decision. So, therefore, when calculating the beta of a company in the pure play method or the method of comparables, we remove the financial risk from the beta of the comparable companies and only take into account the operating beta. The operating beta is then levered up for the risk of the company we are analyzing. The steps to be used are as follows:

Estimate the beta, based upon comparable firms, and after adjusting for risk.

• Step 1: Collect a group of publicly traded comparable firms, preferably in the same line of business, but more generally, affected by the same economic forces that affect the firm being valued.
  • A Simple Test: To see if the group of comparable firms is truly comparable, estimate a correlation between the revenues or operating income of the comparable firms and the firm being valued. If it is high (and positive), of course, your have comparable firms.
• Step 2: Estimate the average beta for the publicly traded comparable firms.
• Step 3: Estimate the average market value debt-equity ratio of these comparable firms, and calculate the unlevered beta for the business.
  • b_unlevered = b_levered / (1 + (1 – tax rate) (Debt/Equity))
• Step 4: Estimate a debt-equity ratio for the private firm. The basic problem, however, is that you have only book values for the private firms. This can be corrected in one of two ways ñ
  • Assume that the private firm will move to the industry average debt ratio. The beta for the private firm will then also converge on the industry average beta. This might not happen immediately but over the long term.

Beta_{private firm} = Beta_unlevered (1 + (1 – tax rate) (Industry Average Debt/Equity))

• Estimate the optimal debt ratio for the private firm, based upon its operating income and cost of capital. Use this optimal debt ratio to calculate the beta. (Be consistent about then using the same debt ratio in your cash flow estimates)

Beta_{private firm} = Beta_unlevered (1 + (1 – tax rate) (Optimal Debt/Equity))

Step 5: Estimate a cost of equity for the private firm, based upon this beta.

Null Hypothesis: The null hypothesis, H0, represents a theory that has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved. For example, in a clinical trial of a new drug, the null hypothesis might be that the new drug is no better, on average, than the current drug. We would write

H0: there is no difference between the two drugs on average.

We either “Reject H0 in favour of H1” or “Do not reject H0“; we never conclude “Reject H1“, or even “Accept H1“. If we conclude “Do not reject H0“, this does not necessarily mean that the null hypothesis is true, it only suggests that there is not sufficient evidence against H0 in favour of H1. Rejecting the null hypothesis then, suggests that the alternative hypothesis may be true.

Alternative Hypothesis: The alternative hypothesis, H1, is a statement of what a statistical hypothesis test is set up to establish. For example, in a clinical trial of a new drug, the alternative hypothesis might be that the new drug has a different effect, on average, compared to that of the current drug. We would write

H1: the two drugs have different effects, on average.

The alternative hypothesis might also be that the new drug is better, on average, than the current drug. In this case we would write

H1: the new drug is better than the current drug, on average.

The final conclusion once the test has been carried out is always given in terms of the null hypothesis. We either “Reject H0 in favour of H1” or “Do not reject H0“.

Note: The equal to (=) sign is always used in the Null Hypothesis.

Test Statistic: A test statistic is a quantity calculated from our sample of data. Its value is used to decide whether or not the null hypothesis should be rejected in our hypothesis test. The choice of a test statistic will depend on the assumed probability model and the hypotheses under question.

Critical Value: The critical value(s) for a hypothesis test is a threshold to which the value of the test statistic in a sample is compared to determine whether or not the null hypothesis is rejected. The critical value for any hypothesis test depends on the significance level at which the test is carried out, and whether the test is one-sided or two-sided.

P-Value: It is equal to the significance level of the test for which we would only just reject the null hypothesis. The p-value is compared with the actual significance level of our test and, if it is smaller, the result is significant. That is, if the null hypothesis were to be rejected at the 5% signficance level, this would be reported as “p < 0.05″.

Small p-values suggest that the null hypothesis is unlikely to be true. The smaller it is, the more convincing is the rejection of the null hypothesis. It indicates the strength of evidence for say, rejecting the null hypothesis H0, rather than simply concluding “Reject H0‘ or “Do not reject H0“.