Calculate the return on equity for each bank

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Reference no: EM131091037

Public Affairs 974 Fall 2012 - Problem Set 2

1. Suppose the price change of a stock is given by:

Pt+1 - Pt = (EtPt+1 - Pt) + [(Dt+2 - EtDt+2/1+rp+rf) + (Et+1Pt+2 - EtPt+2/1+rp+rf)]

Assume no news regarding dividends is coming out between t and t+1.

1.1 Why how might changes in expectations from t to t+1 regarding events at t+4 have an impact on the price change from t to t+1? Be explicit about the channel.

1.2 Should the change in the stock price be a completely uncorrelated random error? Show why or why not.

Q2. Consider a Bank that has the following balance sheet:

2.1 Suppose the bank has the following structure:

Assets

Liabilities

Reserves               $50M

Checkable             $230M Deposits

Securities              $25M

Govt Securities      $25M

 

Loans                    $150M

Bank Capital          $20M

Bank capital is the equity of the owners (shareholders) of the bank. ABS stands for asset backed securities.

Under the Basel II guidelines, government securities would have zero weight in assets; recalculate the capital ratio for this bank. Show your work. (Note also reserves carry zero weight in the calculation of risk weighted assets.)

2.2 Suppose the government securities are actually as risky as non-government securities. Calculate the true capital ratio.

Q3. Leverage, liquidity, and bank balance sheets

3.1 Consider two banks, H (high bank capital) and L (low bank capital).

High Bank Capital

Low Bank Capital

Assets

Liabilities

Assets

Liabilities

Reserves $9M

Deposits       $90M

Reserves $10M

Deposits       $96M

Loans

$71M

Bank Capital $10M

Loans

$70M

Bank Capital $4M

ABS

$20M

 

ABS

$20M

 










Bank capital is the equity of the owners (shareholders) of the bank. ABS stands for asset backed securities.

Calculate the return on equity (ROE) for each bank, if the rate of return on loans is 5%, and 10% on ABS, and the interest rate on deposits is 2%.

3.2 Show what happens to each of the bank balance sheets when the asset backed securities lose 25% of their value.

3.3 Now consider two banks, one which borrows a nothing short term, and one that borrows a lot on short term money markets.

Bank Deposit Based

Money Market Based

Assets

Liabilities

Assets

Liabilities

Reserves $6M

Deposits       $60M

Reserves $3M

Deposits       $30M

Loans       $74M

Short term     $30M

Loans       $77M borrowing

Short term     $60M borrowing

ABS         $20M

Bank Capital $10M

ABS         $20M

Bank Capital $10M

Calculate the return on equity (ROE) for each bank, if the rate of return on loans is 5%, and 10% on ABS, and the interest rate on deposits is 2%, and the interest rate on short term borrowing is 1%.

3.4 Show what each bank must do when short term money markets freeze, so that the banks cannot continue to borrow short term.

Q4. Consider a Taylor rule of the following form:

itFedFunds                = πt + 0.5 x (yt - yt* ) + 0.5 ? (πt - πt*) + rt*

4.1 Calculate the implied Fed funds rate, assuming the equilibrium real rate is 2.5%, and target inflation rate is 2%. You will need to obtain information on the output gap and inflation rate. Show your work.

4.2 Suppose there is uncertainty surrounding the estimates of y-y* and π-π*. Suppose further the standard deviation of each series is 0.026 and 0.012 respectively. What is the range of changes consistent with the Taylor rule, and this degree of uncertainty, using 95% confidence intervals? Show your work. What assumptions do you need to make in order to obtain your answer?

Reference no: EM131091037

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