# CFAI Two Separate Formulas for Human Capital

Hi everyone,

Seems the CFA is out to confuse everyone once more with two separate and conflicting formulas for Human Capital:

Human Capital** t**=j=tT = (pst)(wt-1)_(1+_g) / (1+rf+y)^(t) where p is the probability of survival to year or age, w is income from employment, g is the annual growth rate, rf is the risk free rate, y is the occupational income volatility .

• Human Capital is the present value of expected future labor income.
• Human Capital = Ij / (1+ r )^(j-t) where Ij is expected income at age j of expected future labor income.

I guess the reader will just have to assume which formula the CFA wants based on question context, best of luck.

First is a core capital equation. It can be calculated on nominal or real basis. It is not same as HC.

HC is PV of expected future labor income.

• Consider an Economic BS which is an extension of classical BS for PV of HC.
• Net asset value, both financial and human remain as core capital after funding all expected liabilities.
• This remainder is multiplied by probability of surviving at least one spouse if we consider married couple.
• Then, the sum of future distribution is discounted back to present.
• If the amount of current portfolio covers this discounted core capital, the couple have sufficient funds for additional wishes.
• If you make an inflation adjustment in numerator by discounting, you also have to do same in denominator.

No I believe you are mixing up concepts, please reference CFAI text per below.

Core Capital is discussed in the text Vol II p.281

Human Capital (version 1) is discussed in CFAI text Vol II p. 384

Human Capital (version 2) is discussed in CFAI text Vol III p. 254

Correct, didn’t understand your question. Then both formulas are basically the same. The PV of future HC. Reading 12 is modified version of PV of HC.

So far, solved tons of questions and cannot remember if in any was asked to discount only HC by either approach. But, core capital calculation and probability weightening may appear often.

Yes like I was saying just something the reader will likely have to remember if there is specific context provided, such as “occupational income volatility”

This is some kind of premium added to RF for volatile occupations, isn’t it? For example, for miners or whatever. In some countries, such occupations receive much more governmental guaranteed pension than all others. This is not mentioned in curriculum. Soldiers, too.

That could potentially be a hypothetical application. I was just referring to what CFAI notes as the variables. They are in that blue box problem on Vol II p.384

I thought it’s based on nominal? Based on the book, r is nominal risk free rate. I assume wage growth rate g here includes inflation rate.

Update. Just have taken an AM session. At individual part, there is a risk management individual part (I love so that chapter, lol!), heavily weighted with required future wage discounting and importing into extended BS to get an Economical BS.

I think, your query was related to discount rate and I was pretty correct yesterday. You should just add occupational RP to nominal RF to get discount rate. In nominator, you have compound with wage growth rate^n period and multiply with probability of surviving for each year what is 1 - probability of death for each year. Future wages are nothing else than bond like distribution weighted with probability of survive for each period.

Then sum of PV of such discounted HC you have to add to Financial capital in classical BS to reach Economic BS. There ia also the amount of future pension liability which is also supposed as FC which was not contained in BS so you should also add this amount into BS capital.

It should be based on nominal as plain vanilla. However, core capital may be calculated on real basis. Then both values must be on real basis, not inflation adjusted wage in nominator and discounted by a real RF in denominator.