# After-tax nominal rate of return that is required for the portfolio

Consider the below requiring the after-tax nominal return

Mortgage payments remaining 5 Annual mortgage amount (funded from their investment portfolio) 55,000 Current Investment portfolio value 10,200,000 Required Investment portfolio value 15,000,000

N = 5, PV = -10,200,000, PMT = 55,000, FV = 15,000,000, compute i/y= 8.4y8%

The answer is 8.48, but why do we not x (1+inflation) since we are looking for the nominal return? Isn’t the 8.48% a real amount?

asked, answered.

mortgage pmt is fixed (no inflation therefore)

it is paid with after tax money - so return is after tax nominal when 55K is used directly.

cpk thank you for the response, i understand that the PMT is an after-tax amount. But i remember seeing a post that said whether or not inflation was accounted for in expenses/investable assets, to obtain nominal return then we must x (1+inflation). So still unsure why we don’t x (1+inflation).

The key here is that the mortgage payments are not indexed with inflation, the way other expenses might be. When you calculate an inflation adjusted value for an expense, the assumption is that the expense is X today and {(1+inf)^t }*X in the future. However, for a fixed rate mortgage, the payment is unaffected by inflation.

I have to assume from the information you provided that the future value of the portfolio is also agnostic to the rate of inflation.

Does that make sense?

DJS, i understand that the mortgage payment is fixed and soit does not need to be adjusted for inflation. But I am unclear about why the overall return (8.48%) does not have to be inflation adjusted to obtain the nominal return? This is CFAI 2008 , question 1 Part D ii

see if this helps:

http://www.analystforum.com/forums/cfa-forums/cfa-level-iii-forum/91339628

Specifically it is based on if they need \$15MM in todays dollars or \$15MM total in 10 years:

To add further clarification:

James has a 1,000,000 portfolio and needs \$2,000,000 in 10 years. What is the nominal rate needed? What is the real rate needed? Inflation is 1%.

The Required RoR is 7.18%, and the CFAI calls it “Nominal”. However, that includes a premium for expected inflation? How? I would expect you would need 8.18% nominal (ror + inflation). If inflation was 1000% and you received a 7.18% return, how would you have \$2MM?

Response from s2000:

TIPS (real) + actual inflation = nominal.

The TIPS principal is adjusted by actual inflation, not expected inflation.

As for James, if the \$2,000,000 he needs in 10 years is in then-year dollars, then 7.18% is a nominal return: 6.18% real return, 1% inflation. If the \$2,000,000 he needs in 10 years is in current-year dollars, then 7.18% is the real return and 8.18% is the nominal return. It all depends on what “\$2,000,000” means.

This about it this way, the real return calculation is based on the return needed to cover inflation-adjusted expenses (i.e. the expenses, not including the affect of inflation) whereas the nominal return is the return needed to cover the actual expenses, including the inflation effect.

So, in a ‘normal’ question where the investors expenses are \$100,000, their account is \$2,000,000 and inflation is 2% then we can say that they need 5% return to generate the necessary \$100,000 in expenses (this is the real return) PLUS 2% (or times 1.02) to account for the increase in the expenses due to inflation.

With a fixed mortgage, if you need \$55K you need \$55K - inflation has no affect.

Another way to think about it is, if your needs are inflation insensitive then the EFFECTIVE inflation rate is 0%.

why isnt the investable asset base of 500,000 indexed to inflation? the reading says “investable assets are maintained on an inflation adjusted basis in the future” that would increase asset base by 20k. and thus changes my whole answer for part A… ??

im still with sfad. not really sure why you indexed to inflation for part A but not part D

do you mean to say you have 100\$ in the bank - it will grow to show the current rate of inflation if it justs sits there?

it will not unless your portfolio returns are higher (or include effect of inflation).

ah. gotcha. thx cpk