The Harvard Endowment Fund is well-known for achieving big and reliable returns with a long-term holding strategy. How can you adapt the Harvard Portfolio to your risk tolerance?

We will use our optimizer as we did in my previous articles to make an analysis. But before we proceed let me briefly explain what an optimizer is. An optimizer is a powerful tool that enables you to calculate portfolios that have the least volatility for a given expected return or equivalently, portfolios that have the highest expected return for a given level of volatility *assuming* the data that goes into their calculations are sufficient and they obey the important assumption of normality or near-normality.

## Risk Tolerance

There is a nice short article on risk tolerance at msn moneycentral where a simple definition of risk tolerance was sited: "What is the possibility that I will lose some of my money? Will my $1,000 ever be less than $1,000?"

At the other end of the spectrum are risk tolerance questionnaires like finametrica that claims to be a "Scientifically validated tool for assessing financial risk tolerance".

In the discussion that ensues, I will be looking at 7 portfolios that span the volatility range of the Harvard Portfolio. The Harvard portfolio that we use is a sample and not the full portfolio. The actual portfolio might very well be more optimized than what appears here. According to the Harvard Crimson, current state laws exempt Harvard from disclosing all the holdings in their endowment fund.

A sample portfolio notwithstanding, the lessons that can be drawn from the discussion remain valid.

## The Harvard Portfolio

According to stockpickr.com, Harvard Management Company which is the investment arm of the Harvard Endowment Fund had these securities in it's portfolio at the date stated on their website:

- America Movil SA de CV (AMX)
- iPath MSCI India Index ETN (NYSEARCA:INP)
- Fomento Economico Mexicano SAB de CV (NYSE:FMX)
- HDFC Bank Ltd (HDB)
- Market Vectors Russia ETF (RSX)
- News Corporation (NWS)
- Petrobras-Petroleo Brasileiro S.A. (NYSE:PBR)
- SPDR S&P MidCap 400 ETF Trust ETF (NYSEARCA:MDY)
- Service Corporation International (NYSE:SCI)
- Taiwan Semiconductor Manufacturing (NYSE:TSM)
- United Microelectronics Corp (NYSE:UMC)
- Vanguard Emerging Markets ETF (NYSEARCA:VWO)
- iShares FTSE China 25 Index ETF (NYSEARCA:FXI)
- iShares S&P GSCI Commodity Indexed Trust ETF (NYSEARCA:GSG)
- iShares S&P Latin America 40 Index ETF (NYSEARCA:ILF)
- iShares MSCI Brazil Index ETF (NYSEARCA:EWZ)
- iShares MSCI Chile Index ETF (ECH)
- iShares MSCI EAFE Index ETF (NYSEARCA:EFA)
- iShares MSCI Mexico Index ETF (NYSEARCA:EWW)
- iShares MSCI South Africa Index ETF (NYSEARCA:EZA)
- iShares MSCI South Korea Index ETF (NYSEARCA:EWY)
- iShares MSCI Taiwan Index ETF (NYSEARCA:EWT)
- iShares MSCI Thailand Investable Market Index ETF (NYSEARCA:THD)
- iShares S&P 500 Index ETF (NYSEARCA:IVV)

It is obvious that the Harvard Mix is diversified across many countries and industries. In the discussion that follows we leave out ECH and THD as we only include securities that have a sufficiently long history of data for optimization purposes (i.e. about 3 years data). As always, we do not suggest that the optimized mix is the ultimate. It is simply used as a yardstick to make comparisons.

## 7 Risk Profiles

The graph on the right shows the efficient frontier of the 22 stocks above. It is "efficient" in the sense that every portfolio on the red line has the maximum expected annualized return for any given volatility as well as the minimum volatility for any given expected return.

It is called a "frontier" because no other combination of weights within this portfolio of 22 stocks is more efficient. In other words, no portfolio can exist above the red line. As in my previous article "Portfolio Optimization: Carl Icahn vs. T Boone Pickens vs. Warren Buffett", the white line is a constrained efficient frontier where every stock in the mix must be included with a minimum of 0.5% allocation.

How do you adapt the Harvard portfolio to your risk tolerance? We will use the idea of constraints like the white efficient frontier in the graph above except there will be no minimum allocation. Instead the efficient frontier is constrained to contain the exact proportions of securities in different risk (volatility) categories.

The Low Risk, Medium Risk, and High Risk categories are the lowest one-third, middle one-third, and highest one-third of securities in terms of their volatility. For example, in Profile 3 below, every portfolio on the white frontier is efficient but must constitute 50% Low Risk, 40% Medium Risk, and 10% High Risk securities.

## Profile 1 - 100% Low Risk Securities

The graph on the right shows a Profile 1 efficient frontier (white line) from the Harvard Mix. The graphs on the left show the safety of the portfolio selected. The probability of a negative annualized return over a 5-year holding period for the selected portfolio is 9.06%

## Profile 2 - 70% Low Risk, 30% Medium Risk

The graph on the right shows a Profile 2 efficient frontier (white line) from the Harvard Mix. The graphs on the left show the safety of the portfolio selected. The probability of a negative annualized return over a 5-year holding period for this portfolio is 3.14%

## Profile 3 - 50% Low Risk, 40% Medium Risk, 10% High Risk

The graph on the right shows a Profile 3 efficient frontier (white line) from the Harvard Mix. The graphs on the left show the safety of the portfolio selected. The probability of a negative annualized return over a 5-year holding period for this portfolio is about 1%

## Profile 4 - 30% Low Risk, 40% Medium Risk, 30% High Risk

The graph on the right shows a Profile 4 efficient frontier (white line) from the Harvard Mix. The graphs on the left show the safety of the portfolio selected. The probability of a negative annualized return over a 5-year holding period for this portfolio is about 0.7%

## Profile 5 - 10% Low Risk, 40% Medium Risk, 50% High Risk

The graph on the right shows a Profile 5 efficient frontier (white line) from the Harvard Mix. The graphs on the left show the safety of the portfolio selected. The probability of a negative annualized return over a 5-year holding period for this portfolio is about 1.4%

## Profile 6 - 30% Medium Risk, 70% High Risk

The graph on the right shows a Profile 6 efficient frontier (white line) from the Harvard Mix. The graphs on the left show the safety of the portfolio selected. The probability of a negative annualized return over a 5-year holding period for this portfolio is about 3.9%

## Profile 7 - 100% High Risk Securities

The graph on the right shows a Profile 7 efficient frontier (white line) from the Harvard Mix. The graphs on the left show the safety of portfolio selected. The probability of a negative annualized return over a 5-year holding period for this portfolio is about 10.3%

## What are the lessons

1. The probability of a negative annualized return over a 5-year holding period for the Profile 1 portfolio is 9.06%. Increasing the risk tolerance to Profile 2, however, decreased the probability of a negative annualized return to 3.14%. Shouldn't this probability increase with increased portfolio volatility?

It depends on which portfolio in Profile 2 you chose. For the particular portfolio chosen in the example above, the increase in the expected return was accompanied by a less than proportionate increase in its volatility. *Lesson:* If you want to know if your $1000 will ever be less than $1,000 you need to know the real relationship between risk and return for your universe of investments.

2. Each profile has its own efficient frontier and depending on how the universe of securities spreads itself out, these frontiers can overlap. *Lesson:* If you are invested in a fund or mirroring the securities a fund invests in, you may not be able to tell if you are taking on more risk than you can bear unless you integrate the risk-return map of the investment universe of the fund with your tolerance for risk. Tools exist than can help you with this. Readers can check out MorningStar.com's Asset Allocator or the expertGTC3 on Facebook.

3. The universe of 22 securities gets increasingly volatile the higher the expected return. *Lesson:* Having more securities does not necessarily mean greater diversification if the securities you are adding are highly correlated in the positive direction. For example, the following pairs of securities all have correlation coefficients that have stabilized to 98% or higher:

- Vanguard Emerging Markets ETF & iShares S&P Latin America 40 Index
- iShares MSCI Brazil Index Fund & iShares S&P Latin America 40 Index
- SPDR S&P MidCap 400 ETF Trust ETF & iShares S&P 500 Index ETF
- iShares MSCI South Korea Index ETF & iShares MSCI Taiwan Index ETF
- America Movil SA de CV & iShares MSCI Mexico Index ETF

## In Conclusion

Almost everyone knows Harvard University is one of the premier names in the world of college academia. What most of the world may not realize, however, is that the geniuses managing its $27.6 billion endowment have become the envy of other Wall Street fund managers.

When adapting the Harvard or indeed anybody's portfolio to our needs, however, we must be careful to avoid the "one-size-fits-all" notion in regard to risk tolerance and we must be especially aware that "more is not necessarily better" when it comes to diversification.

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