Human capital

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Financial theory

Economists use the term human capital to describe the present value of future labor income.[1] 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).[2] 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:

PV100k30yrs.jpg

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

Equation2.6.png

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

Equation2.6-solved.png

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

Role in investing

Asset allocation versus age

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.[4]

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.[5] 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.

Asset allocation versus income volatility

Not all occupations provide bond-like human capital. Other occupations generate more variable employment income, generating an almost stock-like human capital.[6]

An investor’s human capital can be viewed as a “stock” if both the correlation to a given financial market subindex and the volatility of the labor income are high. It can be viewed as a “bond” if both the correlation and the volatility are low. In between these two extremes, human capital is a diversified portfolio of stocks and bonds, plus idiosyncratic risk.[6]

Investors whose human capital is bond-like can afford to take more risk with their financial portfolio (own more stocks). Investors whose human capital is stock-like should probably be more conservative in their asset allocation.[7]

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.[6][8] 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.[8]

Hum-cap-lif-ins1.jpg

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[9], 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.[10] 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:[11]

Equation2.15.png

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:

Equation-page159.png

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:

Equation-page159-bis.png

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

Choosing a discount rate

In the above examples, discount rates have been provided without justification. The discount rate influences the human capital calculation result, so it is important to carefuly estimate the appropriate discount rate.

Benzoni and Chyruk (2015)[12] write that since human capital is a non-traded asset (in the modern world), its implicit value depends on the preferences of the owner of the asset, not only on the market. Yet we need a way to pick a relevant discount rate.

Blanchett et al. (2016)[13] propose that the nominal discount rate is the risk-free interest rate (e.g., a current treasury bill yield) plus an adjustment based on occupational income volatility. This is an interesting approach, but unfortunately they don't explain how to estimate the adjustment based on income volatility.

See also

References

  1. ^ Bodie, Merton (2000). Finance. Prentice-Hall, p. 146 (ISBN 978-0133108972)
  2. ^ Discounting translates the future income amount to an equivalent amount of income today.
  3. ^ See for example equation 2.6 in Chapurat N, Huand H, Milevsky MA (2012) Strategic financial planning over the lifecycle. Cambridge University Press (ISBN 0521148030)
  4. ^ Bernstein (2010), The Investor's Manifesto. John Wiley & Sons, Inc., p. 76 (ISBN 978-0470505144)
  5. ^ Cocco JF, Gomez FJ, Maenhout PJ (2005) Consumption and Portfolio Choice over the Life Cycle, Review of Financial Studies v. 18, p. 491-533, DOI 10.1093/rfs/hhi017, PDF available on Google Scholar, viewed July 24, 2023.
  6. ^ a b c Chen P, Ibbotson RG, Milevsky MA, Zhu KX (2006) Human capital, asset allocation, and life insurance. Financial Analysts Journal 62:97-109, DOI 10.2469/faj.v62.n1.4061, available on SSRN
  7. ^ Milevsky M (2003) Is your client a bond or a stock? Advisor's Edge, November 2003, p. 22-28, viewed July 25, 2023.
  8. ^ a b Moshe Milevsky (March 30, 2010). "The lowdown on insurance salesmen and warranty peddlers". The Globe and Mail. Retrieved January 21, 2017.
  9. ^ see page 158 in Chapurat N, Huand H, Milevsky MA (2012) Strategic financial planning over the lifecycle. Cambridge University Press, 367 p. (ISBN 0521148030)
  10. ^ see page 159 in the same textbook.
  11. ^ see equation 2.15 in the same textbook.
  12. ^ Benzoni L, Chyruk O (2015) The Value and Risk of Human Capital, Annual Review of Financial Economics 7:179-200, DOI 10.1146/annurev-financial-110613-034406, preprint available on SSRN as Federal Reserve Bank of Chicago WP 2015-06, viewed August 6, 2023
  13. ^ Blanchett DM, Cordell DM, Finke MS, Idzorek T (2016) Risk Management for Individuals, CFA Institute, viewed July 25, 2023.

External links

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