Question

Heather Marks is a trader on the principal investing desk at Barclay’s Bank.
She buys 1,000 units a 7-year, 7% annual fixed coupon mortgage-backed security at par ($1,000).
She finances 50% of the purchase with the bank’s equity and the rest through the repo market. She holds the securities for one year and then resells them at even par after receiving the coupon. Assume that the implied average “repo” rate was 3% for the year.
1) What is the net profit (loss) in dollars, ROA (%), and ROE (%) for this particular deal?
2) Same question but now assume that, instead of 50%, Heather finances the bonds with only 10% equity.
3) Same question and assumption as in 2), but now further assume that, instead of reselling the securities at $1,000, she sells them at$1,050 each.
4) Same as above, but now bonds are resold at $900.
5) How can your results from this problem partly explain the 2008 financial crisis?

Answer 1

Assumption:

--Numbers are rounded off to nearest value

-- #% is considered as cost of capital . Hence 3% is used for conversion to presnt value

1.Answer

At the intial date:

purchase value= $1000( financed by 50% via bank equity(ie $500)&remaining from repo market with 3% interest rate..

After a year:

sale value=$1000(inflow)

coupon received=$1000*7%=$70(inflow)

interest on repo=$500*3%=$15(outflow)

presnt value for the amount received after a year =1000+70-15=1055/1.03=$1024

Net profit=$1024-$1000=$24

ROA%=Return before interest /total value of asset=(($1000+$70)/1.03)-1000)/$1000

=($1038-$1000)/$1000=3.8%

ROE%=netprofit/ equity

=$24/$500=4.8%

2)Answer

At the intial date:

purchase value= $1000( financed by 10% via bank equity(ie $100)&remaining from repo market with 3% interest rate.

After a year:

sale value=$1000(inflow)

coupon received=$1000*7%=$70(inflow)

interest on repo=$900*3%=$27(outflow)

presnt value for the amount received after a year =1000+70-27=1043/1.03=$1013

Net profit=$1013-$1000=$13

ROA%=Return before interest /total value of asset=(($1000+$70)/1.03)-1000)/$1000

=($1038-$1000)/$1000=3.8%

ROE%=netprofit/ equity

=$13/$100=13%

3)Answer

At the intial date:

purchase value= $1000( financed by 10% via bank equity(ie $100)&remaining from repo market with 3% interest rate.

After a year:

sale value=$1050(inflow)

coupon received=$1000*7%=$70(inflow)

interest on repo=$900*3%=$27(outflow)

presnt value for the amount received after a year =1050+70-27=1093/1.03=$1061

Net profit=$1061-$1000=$61

ROA%=Return before interest /total value of asset=(($1050+$70)/1.03)-1000)/$1000

=($1087-$1000)/$1000=8.7%

ROE%=netprofit/ equity

=$61/$100=61%

4)Answer

At the intial date:

purchase value= $1000( financed by 10% via bank equity(ie $100)&remaining from repo market with 3% interest rate.

After a year:

sale value=$900(inflow)

coupon received=$1000*7%=$70(inflow)

interest on repo=$900*3%=$27(outflow)

presnt value for the amount received after a year =$900+$70-$27=$943/1.03=$916

loss =$916-$1000= -$84

ROA%=Return before interest /total value of asset=(($900+$70)/1.03)-1000)/$1000

=($942-$1000)/$1000= -5.8%

ROE%=netprofit/ equity

=-$84/$100=-84%

5)Answer

From all the above scenarios ,we can see that there is high ROA when there ishigh sale value, and high ROE when debt is more . The interest rate in the market is to be prevail on good terms unless there is change in rate. The reason behind 2008 crisis is defaultin interest payments,which it can be override by the user friendly interest rate.