Asset Valuation

PART Ⅰ

In this report we will analyze the financial position and the interest rate risk exposure of ABC Bank.

Balance Sheet for ABC Bank

Part 1.1 Calculate the Overall Macaulay Duration

To analyze the interest rate risk on the “Net Worth” (market value of equity), we first calculate the overall Macaulay Duration.

Because the Macaulay Duration is DMacaulayportfolio=i=1Nwi*DMacaulayBond(i),

We can conclude that:

The Macaulay Duration for the bank’s asset equals to value weight of different components of asset* Macaulay Duration of different components of asset:

DMacaulayAsset=0.35*0+0.1*3+0.3*10+0.2*3.5+0.05*0=4

The Macaulay Duration for the bank’s liability equals to value weight of different components of liability* Macaulay Duration of different components of asset:

DMacaulayLiability=0.8235294*2+0.1764706*3=2.17647059

Also we can calculate the Duration Gap by this function:

DURMacaulayGap=DMacaulayAsset –LA*DMacaulayLiabilities =EA*DMacaulayEquity ,

= 4-(170/200)*2.17647059=2.15

Therefore, the Macaulay Duration for the bank’s net worth (equity) is:

DMacaulayEquity=2.15*200/30=14.3333333.

Part 1.2 Calculate the Duration Gap

The Duration Gap for ABC Bank is 2.15, as is calculated in Part1.1, which is a positive number. By definition, the duration gap measures the change in net worth in a percentage of asset value with respect to the interest rate change.

DURMacaulayGap=DMacaulayAsset –LA*DMacaulayLiabilities

The duration gap will be a positive number if the duration of assets is larger than the duration of liabilities. In this case, when interest rate rises, ABC bank’s assets will lose more value than ABC bank’s liabilities. As E=A-L, the value of the firm's equity will be reducing. On the contrary, when interest rate falls, ABC bank’s assets will gain more value than ABC bank’s liabilities. As a result, the value of the firm's equity will increase.

Given that the equity takes a tiny proportion of total asset in...