ASSET ALLOCATION
The two key building blocks of modern finance are:
1. Mean Variance Optimization: When making investment decisions, investors set their allocation such that the expected return is maximized for a
given level of risk.
2. Capital Asset Pricing Model (CAPM): The expected return on an asset is proportional to its systematic risk (i.e. beta)
Mean Variance investors like higher expected returns but dislike risk, therefore, there is a trade-off between risk and return. In the set of portfolios available,
the Efficient Frontier is the set of optimal portfolios that offer the highest expected return for different levels of risk, or alternatively, the lowest risk for
varying level of expected returns, given a particular set of assets.
Topic 1: Strategic Asset Allocation - Harvard Management Company (HMC) Endowment Case
There are two types of Strategic Asset Allocation:
Strategic Asset Allocation entails long-term/benchmark allocation to broad asset classes. This asset allocation maximizes the risk-return trade-off given
inherent risk/return asset class characteristics. We calculate it using the long-term average expected return and volatility of the asset, rather the current values.
Fund managers stick relatively close to their SA and remain rather passive in their implementation.
80%-90% of time-series variation in a typical mutual fund/pension fund’s performance over time is the result of its strategic asset allocation policy. On the
other hand, 35%-40% of the cross-sectional variation in 10-year fund returns is the result of its strategic asset allocation policy. Some other factors that affect
the variation of fund returns include: asset-class timing, style within asset classes, security selection, and fees.
Tactical Asset Allocation is an active strategy to deviate from the long-term allocation based on changing market circumstances. It is all about “market
timing”. We tilt weights toward assets we expect to do well. The most important decision is how much weight each of the asset classes will have in your
portfolio.
The main examples of asset classes include: Traditional: Cash, Bonds, Equities; and Alternatives: Private Equity, Private Debt, Hedge Funds, Real Estate,
Crypto-currencies, Commodities
Harvard Management Company (HMC) Endowment
The Endowment Policy Portfolio is the asset mix that is expected to meet the University’s long-term return goals with the appropriate level of risk. The
Policy Portfolio was composed of 71% Equity and 31% Alternatives.
The role of the policy portfolio for HMC is to achieve a long-run (or ‘strategic’) asset allocation of the endowment over main asset classes, and have a
benchmark for performance measurement for the endowment and the managers. The policy portfolio is determined using quantitative techniques. First, you
specify the objective (utility) function, then specify the asset classes you want to include in the portfolio, make capital market assumptions on the Expected
Returns, Volatilities, and Correlations, and lastly optimize the portfolio (with or without constraints).
We want to know whether it is beneficial for HMC to add inflation-linked bonds as an additional asset class. Before answering this, we want to look at
the rationale for current allocation, discussing the importance of equity exposure, and the importance of diversification (across individual stocks, across
countries, and alternative assets).
Equity Participation Puzzle
Around 50% of US households with positive wealth do not hold stocks, and there is a great under-participation in equity, despite there being a 5.5% premium
on equity returns compared to bond returns. Over short-horizons equities are definitely riskier than bonds, but does that matter to a long-term investor?
We might believe that this is due to a high risk-aversion of individuals. However, using Mean-Variance Allocation we see that, no matter what risk-aversion
level we choose, even for unrealistically high risk-aversion levels, we still get a 20% allocation to equities. Therefore, MVA cannot explain the equity under-
participation that is evident in the market.
Behavioral Finance
As MVA is not able to explain the under-participation in the equity market, we look at behavioral finance. Behavioral preferences, or non-standard preferences,
are those that move away from rational behavior. Literature claims that risk taking tends to increase with wealth, IQ, financial literacy, and trust in financial
institutions and systems; whereas it tends to decrease with past bad experiences.
1. (Myopic) Loss Aversion:
a. Loss Aversion entails that investors feel relatively worse about losses that they feel good about gains. Thus, they avoid assets with
large negative tails, such as stocks.
b. Myopia (short-sightedness) entails that investors tend to check the value of their portfolio far too regularly (vigilance). In this case,
the reference point is not the amount that was initially invested, but rather, the amount that the investor had at the best time.
2. Probability Overweighting: Investors tend to overweight extreme events (relative to the objective or observed probability). For instance,
overestimating the likelihood of winning the lottery or dying in a plane crash. Investors tend to attach a too high probability to crash in the equity
market, and a too low probability to a positive equity return going forward.
,Rule 1: Do not Neglect Equities: Probability overweighting increases the perceived likelihood of both extreme positive and negative events. For sufficiently
loss-aversion investors though, only the increased likelihood of the left tail will matter, and thus, they avoid equities altogether.
Rule 2.a: Diversify Idiosyncratic Risk
Harry Markowitz identifies two types of risk:
1. Systematic risk which refers to the risk inherent to the entire market or market segment, and it is undiversifiable. Systematic risk is also known
as the market volatility or risk, and it affects the overall market.
2. Firm-specific or Idiosyncratic Risk can be diversified as it is specific to only one firm. Portfolios with large amount of idiosyncratic risk are
inefficient as the investor does not get compensated for bearing the firm-specific risk, thus, they should diversify it away.
Rule 2.b: Diversify Internationally: Is there value in diversifying equity portfolios internationally? If so, why is there an extreme home-bias in investment
portfolios? (>80% in home stocks). Data shows that you can reduce the volatility of your portfolio quite a bit by investing in international stocks. An allocation
of between 40-50% to foreign stocks seems appropriate. However, we also observe that the reduction in volatility is smaller for the US compared to other
markets.
There are reasons to believe the correlation between economies and thus, cash flows has gone up over time. This may be due to the global equity market
which means that all markets are exposed to the to the same market sentiment through discount rate. Information technology has helped as now everyone
can buy stock from abroad, access it, and get information on it. Thus, asymmetric information has decreased.
Long-horizon investors benefit substantially from international diversification as (1) discount rate shocks are mean-reverting rapidly, and hence do not
increase long-horizon correlations; and (2) cash flow shocks are highly persistent and can lead to permanently higher long-horizon correlations, but studies
do not find these shocks to be highly-correlated.
Rule 2.c: Emerging and Frontier Markets as Diversifiers: There is a growing gap between emerging markets and developed markets. Before 2008, margins
for the two indices were similar, but unlike American stocks, emerging-market profits never recovered.
But what makes an investment in these markets attractive? High growth expectations do not necessarily mean that it is a good investment, as high growth is
already embedded in the current market valuations and the stock’s price. The reason to invest in these markets is high risk premia, specifically: political risk
premium, geopolitical risk premium, liquidity risk premium, and currency risk premium. Regarding diversification, correlations seem to have decreased since
2008 for all markets.
Rule 3: Diversify into other asset classes: The Endowment model states that investing is characterized by highly-diversified, long-term portfolios that differ
from a traditional stock-bond mix in that they include less-traditional and less-liquid asset classes, such as PE and real estate.
Hedge Funds seek risk and aim to outperform a benchmark, but they are less regulated, have high costs, performance fees, and operational costs, and they
are also highly-levered (i.e. they borrow money to make risky investments). At first, investors were better-off investing in the S&P 500 than in Hedge funds.
Further, hedge funds performance during the crisis was very mixed, they missed the recovery period, and didn’t show much market-timing capability.
Private Equity is equity of companies that is directly sold to investors (rather than on an organized exchange), thus, there is no daily trading. Private equity
is composed of illiquid investments with a horizon of 5-10 years (or more). There is a very diverse set of underlying equity: leveraged buyouts (i.e. you buy
a firm with debt, but the firm owns a stable cash flow that will help you pay back the debt), growth equity, venture capital, real estate, special debt, etc.
A PE fund buys stakes in private equity, typically using 1/3 own equity and 2/3 debt financing. Like hedge funds, private equity funds are mostly held by
sophisticated investors, like pension funds or endowments, and are therefore less regulated.
Private equity is attractive because investors earn an illiquidity premium (for locking their money for 5-10 years) as it is hard to find potential buyers, and
thus, they get compensated for it. Because PE firms tend to own substantial stakes and longer investment horizons, they have the capacity to better control
firms, and turn sluggish businesses into world-beaters. However, it is difficult to assess whether PE firms live up to the high expectations in terms of returns,
as with the absence of market prices (non-listed firms), it is not straightforward to measure returns or volatility.
Estimates vary widely across studies and types of PE, however, there is some consensus that:
- PE outperforms standard public equity benchmarks, at least before costs
- PE’s performance has gone down in the last decade, to levels that bring it to par with the S&P 500 (suggesting that illiquidity premium is small)
- When PE performance is compared to more appropriate benchmarks (e.g. index of small-value firms), PE often underperforms
Despite decreasing returns, a lot of money has flown into PE funds lately. This may be due to the fact that investors seek leverage. You want to take on
additional risk, but are limited to do so (e.g. because regulation or internal rules prevent you from doing so). Further, you can implicitly take on leverage by
investing in PE rather than S&P 500. (of every $ invested in PE, 0.67$ is borrowed).
Investors appreciate that PE returns are artificially smooth. As PE firms are not listed, and their valuations tend to rely on self-appraisal, PE returns are
not as volatile as public market returns. A portfolio that mixes public with private equity will look less risky, at least in the short term. The manager of such
mixed fund is less likely to be forced to sell at rock-bottom prices because of imposed risk constraints or solvency rules (which tend to become binding when
volatility goes up).
Real Estate is the largest alternative asset class. It can be of two types: Residential and Commercial. The different ways to invest in real estate include:
- Direct purchase of property
, - Participation in private real estate fund
- Listed Real Estate Investment Trusts (REITs)
- Other (fund-of-fund, limited partnerships, ETFs)
Pros Cons
Attractive risk-return trade-off REITs come with substantial volatility
Potential for reliable income Market is very exposed to housing prices bubbles
Rent and coupons follow inflation Correlation with the equity market is now between 0.6-0.8 (high)
Commodities are basic goods of comparable quality (despite the producers) used in commerce or manufacturing. There are four basic groups: energy,
metals, livestock, and agriculture. Before, commodities were mainly traded between producers and firms using them as input in their production. Now,
investors take exposure by means of futures contracts (no physical delivery). Commodities are attractive as the correlation with equity market is almost 0.
Gold has two prominent perceived qualities: (1) is an inflation hedge; and (2) provides a hedge against “bad times”. However, if gold were a good inflation
hedge, then its real value should be constant over time (aka the “golden standard”). However, gold price is much more volatile than inflation. Data shows
that there is no clear relationship between gold and unexpected inflation. In 2022, gold price should have risen with inflation, but instead it dropped. Over
the very long term, gold keeps your purchasing power intact, however, it is not a good hedge against inflation.
Crypto Currencies are believed to be the new gold (inflation hedge, safe haven). However, over time, Bitcoin has become highly correlated with the
overall equity markets. For a hedge asset, we would want very poor correlation with the equity market. There are several concerns regarding crypto, (1)
environmental concerns regarding mining; (2) issues with stablecoins (Luna/Terra collapse); and (3) lack or threat of regulatory oversight.
Treasury Bonds are a more mundane suggestion regarding diversification. Bonds did very well over the last decades, as they are negatively correlated
with equities. In the ‘80s and ‘90s, there was a positive correlation between bonds and the equity market. However, around the 2000s, the correlation became
negative, making bonds a good hedge against risk. The Sharpe Ratio of portfolio with a ratio of 40-60 equity to bonds has a higher Sharpe Ratio than an
equity portfolio. The ratio gets even better with time.
Whether Treasury Bonds serve as a hedge against equities or not depends on the cyclical nature of inflation:
1. Inflation is countercyclical (i.e. supply-shock dominates): positive inflation shock signals bad news about the future economy. Equities drop in
value because of lower-than-expected growth prospects, whereas bonds drop because higher-than-expected inflation raises yields. Thus, there is
a positive stock-bond correlation.
2. Inflation is procyclical: positive inflation shock signals good news about the future economy. Equities surge because of better-than-expected
growth prospects; and bonds drop because higher-than-expected inflation raises yields. In this case, there is a negative stock-bond correlation.
E.g. higher-than-expected inflation signals the economy picking up, or lower likelihood of deflationary nightmare regime.
Currently, we are in a countercyclical state of inflation, and while the 60-40 portfolio were a good idea some time ago, nowadays they are not as profitable.
HMC Endowment
Looking back at the case, our task is to consider adding another asset class to the HMC current policy portfolio. Should HMC add inflation-linked bonds to
its portfolio? If yes, how much? What are the characteristics that would make this an interesting asset to invest in? In order to answer these questions, we
will first try to understand the asset.
E.g. Consider a 10-year nominal bond with an annual coupon of 3%. The yield composition is as follows:
Where risk premium is made up of: Real Rate Risk Premium and Inflation Risk Premium.
→ if inflation remains at 2%, you get more than just inflation compensation, you get compensation for the risk
However, if inflation increases to 3%, the sum of the real value would be equal to 100, thus, no risk compensation.
On the other hand, if the inflation increased even more, you would lose. Therefore, Nominal Bonds are a poor hedge against
inflation, which is the main risk for long-term investors.
On the other hand, if we consider inflation-linked bonds, their yield is composed of the real rate and the real rate risk premium, as the inflation risk is
eliminated.
E.g. Consider a 10-year inflation-linked bond with an annual real coupon of 0.65%. Assume inflation remains at 2%. Nominal coupons increase over time
as inflation increases, whereas the real coupons remain constant.
