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Regression Analysis of Life Insurance Company

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A life insurance company wishes to examine the relationship between the amount of life insurance held by a family and family income. From a random sample of 20 households, the company collected the data in the file insur.xls. The data are in thousands of dollars.

(a) Estimate a linear relationship between life insurance (Y) and income (X).
(b) Discuss the relationship you estimated in (a). In particular:

i. What is your estimate of the resulting change in the amount of life insurance when income increases by $1000?

ii. What is the standard error of the estimate in (i), and how do you use this standard error for interval estimation and hypothesis testing?

iii. One member of the management board claims that for every $1000 increase in income, the amount of life insurance held will go up by $5000. Choose an alternative hypothesis and explain your choice. Does your estimated relationship support this claim? Use a 5 percent significance level.

(c) Test the hypothesis that as income increases the amount of life insurance increase by the same amount. That is, test the hypothesis that the slope of the relationship is 1.

(d) Predict the amount of life insurance held by a family with an income of $100,000.

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Solution Preview

You can find the linear relationship (regression) in the Excel file I'm attaching. I ran the Data Analysis toolpack from Excel.
[The output is in Spanish, but I translated the relevant table -the third one- into English]

The equation that gives this regression is basically:

Insurance = 6.85 + 3.88*Income
[Insurance and Income expressed in thousands]

Question b

i) The coefficient associated to income (3.88) shows the change in insurance when income changes by $1. Therefore, for each $1 increase in income, according to this regression, insurance should increase by $3.88. Thus when income rises by $1000, insurance should rise by $3,880.

ii) The standard error of the estimate is part of the output of the regression. In this case, it is 0.1121...

We'll see how to build confidence intervals and perform hypotheses testings in the next questions. However, let's see first a very important fact that we'll use then. Let's call Beta(est) to the estimated coefficient associated to Income, Beta(pop) to the population coefficient (the one we're trying to estimate), SE to the standard error of the estimated coefficient (0.1121... in this case), and n to the sample size (in this case, 20). We have that:

Beta(est) - Beta(pop)
------------------------- follows a T distribution with n-2 degrees of freedom (df)
[obviously, 18 df in this ...

Solution Summary

Predict the amount of life insurance.

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Please be as detailed as possible.

Here is the assignment:

Using the publicly traded company (Genworth Financial) identified and approved during Week One, submit one report with three 1,050-1,400-word sections regarding that company's long-term financing policies and capital structure (section 1), risk management policies (section 2), and an acquisition analysis for that same company (section 3). Please note the last requirement of the acquisition analysis and its association with the risk portion of the report.

Section 1: Report on the company's long-term financing policy & capital structure.

a. Identify the firm's most recent long-term financing decision (e.g., debt, IPO, seasoned equity offering, secondary offering). Analyze the economic, business, and competitive background in which the financing occurred, and identify cost and risk trade-offs.

b. Identify your firm's book value, market value, and levered value according to the M&M model. For a 20 percent increase in assets, perform a quantitative analysis and recommend the optimal capital structure mix for your company. Your analysis should include an estimation of that company's cost of capital, price per share, and market value of the firm.

c. Discuss what changes you think would occur to your finance policy and capital structure if your firm was forced to consider re-organization and bankruptcy strategies.

d. Assume that your firm will be investing in the global market. What international investment and financing opportunities would you consider - and why? Also, discuss foreign exchange risk and give an example that analyzes how foreign exchange rates could cause a loss to the firm.

Section 2: Use the following list of risk management tools and describe the circumstances under which they would be applied to the risk categories of corporate (including risk associated with acquisition analysis and capital budgeting), economic, foreign currency, political, and other relevant global business risks.

e. Black-Scholes options pricing model

f. Simulation analysis

g. Hedging

h. Feel free to add other tools that you find that are relevant to your chosen company.

Section 3: This will be a report to the board of directors that identifies a synergistic acquisition candidate for your company.

i. This report should clearly identify the following:

1) Your proposed acquisition terms

2) Price

3) Financing

4) Potential negotiation strategies

j. Supporting financial data should include the following:

1) Price/earnings ratios

2) Book value

3) Current market value

4) Liquidation

5) Diluted price per share

6) Capital Budgeting tools learned from FIN 544 (NPV, IRR, Profitablility index, payback - optional: Discounted Payback and Modified Internal Rate of Return)

k. Discuss the general risks inherent in an acquisition strategy.

l. Discuss the specific risks that should be included in the quantitative analysis. For example, what risk factors should be included in the discount rate (sometimes known as the hurdle rate, or required rate of return).

Note: Use MS Excel® spreadsheets as support showing your computations where applicable.

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