Human capital

Economists use the term human capital to describe the present value of future labor income. What does this mean and what does it have to do with investing or insurance?

Labor income is the income earned from labor; e.g., job income or salary.

Present value, as it applies to human capital, is today's value of future income, discounted by an assumed interest rate (discount rate). The discount rate depends on the time value of money.

This article first presents some calculation examples to illustrate the concepts of human capital and present value. Then it explores the role of human capital in investing, specifically for asset allocation decisions. Finally it explains how human capital can be used to estimate life insurance needs.

Calculation example
For example, assume a constant, after-tax, real (inflation adjusted) annual labor income of $100,000. At a real interest rate of 0%, the human capital represented by 30 years of this future labor income is $100,000 x 30 = $3,000,000. At higher real interest rates, the present value of the future income is less, since it must be discounted by the real interest rate:


 * Using a real discount rate of 3%, the present value of annual income one year from now is $100,000 ÷ 1.03 = $97,087.
 * The present value of cumulative annual income two years from now is $97,087 + ($97,087 ÷ 1.03) = $191,347.
 * The present value of 30 years of this future real income, discounted at a real rate of 3%, is $1,960,044.

The last figure can be arrived at in Excel using the present value (PV) formula, with a negative payment:


 * [[Image:PV100k30yrs.jpg|500px]]

Or expressed mathematically, we can use the present value of an annuity factor (with constant payments):


 * [[Image:Equation2.6.png|250px]]

where v is the valuation rate, is N is the number of payments. With v = 3% real and N = 30 years, the PVA factor is:


 * [[Image:Equation2.6-solved.png|400px]]

which, multiplied by the annual salary of $100k, yields the same number as before for gross human capital.

Role in investing
A common investing guideline is to decrease the portfolio's ratio of equity securities (stocks) to debt securities (cash and bonds) as one ages. The rule of thumb of holding one's "age in bonds" is an example. One rationale for this is that human capital can be thought of as an inflation-indexed bond.

Young investors typically have much more human capital than financial capital (the value of their savings and investments). Considering human capital as bond-like enables young investors to take more risk by allocating more of their portfolio to stocks. Younger investors have many years to transform part of their human capital into financial assets by saving and investing. They also have more opportunities to use the savings generated by their human capital to buy stocks when prices decline.

Older investors have less human capital, and therefore cannot afford the risk of higher equity allocations. They have less time to transform their human capital into financial assets; i.e., less time to earn, save, invest, and take advantage of stock market declines.

Role in insurance
When you are young, your main asset is your human capital. If you have dependents, you want to protect your future earnings by buying enough life insurance. For young Canadians, human capital is a large number (see the calculator under External links), and buying life insurance with such a large death benefit is only affordable by choosing term insurance.

As time passes, human capital is progressively depleted (you have fewer years of work ahead), and hopefully financial assets accumulate in preparation for retirement and perhaps the children's education. Therefore, your life insurance needs decrease, possibly reaching zero upon retirement, if all your assets can be transferred to your spouse.



Note that if you use human capital to estimate life insurance needs, you could use your after-tax salary, because the death benefits are not taxable, although if the death benefit is invested in a non-registered account, interest, dividends and capital gains will be taxable. Furthermore, you could subtract the present value of your subsistent consumption (the minimum you need to survive on) from your gross after-tax human capital, yielding the net after-tax human capital. This figure is considered an upper bound for estimating life insurance needs.

Detailed example
The following example is from Chapurat et al. (2012), page 159. We want to estimate life insurance needs based on the net after-tax human capital approach. The person is 30, will work to age 65 and will die 20 years later. Initial salary is $50k before tax (to be paid at year end), or $37.5k after tax, growing at a real (after inflation) rate of 0.5% per year. Suppose that the real valuation rate is 2% per year. Subsistent consumption is $12k a year, indexed for inflation.

The first step is to calculate the gross after-tax human capital at age 30. We cannot use exactly the same PVA equation as above, since the income is growing slightly faster than inflation, rather than at 0%. So the calculation uses the present-value-of-annuity factor for a delayed constant-growth ordinary annuity:


 * [[Image:Equation2.15.png|400px]]

where g is the growth rate of payments, v is the valuation rate, is N is the number of payments. Using the supplied numbers and multiplying the PVA factor by the initial after-tax salary, we get a bit over a million dollars:


 * [[Image:Equation-page159.png|600px]]

But the person does not need a million dollars in life insurance because some of this human capital will be used for subsistent consumption if the person does not die prematurely. The present value of the subsistent consumption (or implicit liabilities, IL) to age 85 is about $400k, based on multiplying the annual liability by the PVA factor for an annuity with constant payments:


 * [[Image:Equation-page159-bis.png|400px]]

The net after-tax human capital is $613.4k, so the person could get an initial term life insurance coverage of $600 or $625k based on this approach.