Individuals start investing by buying one stock, and gradually adding more. This ultimately leads to a portfolio that can contain multiple stocks, bonds, and other assets like gold. Small-, mid- and large-sized portfolios are maintained not only by individual investors but also by professional money managers. A portfolio, which essentially is a mixture of multiple securities held together, offers benefits as well as risks. The common proverbs – “Don’t put all your eggs in one basket” or “Don’t trust all your goods on one ship” – explain the concept of diversification that reduces asset-specific risk. The idea is that in a portfolio of 10 stocks, if three stocks under-perform, the remaining seven can cover for them. Such risk, which can be reduced by diversification, is known as unsystematic risk or residual risk of a portfolio.

However, diversification alone cannot eliminate all risk from investments. Correlation between stocks can lead to loss, even with a well-diversified portfolio. In extreme cases, the overall market may tank due to macro-economic factors such as interest rate changes by the US Federal Reserve Bank (the Fed), recessions or slowdowns, or economic uncertainty due to developments like war, rendering diversification ineffective. This constitutes the systematic risk or market risk. (Related: Understanding Systematic and Unsystematic Risk)

This article discusses a few scenarios with examples on how one can protect the overall portfolio by using futures (and options) with an aim to reduce the systematic or market-specific risk.

**Beta (Market Risk Indicator)**

Since the focus is on reducing the systematic or market-specific risk, an efficient indicator of market risk is required for quantitative study. The beta of the portfolio is a measure of systematic risk or volatility relative to the overall market against which the portfolio is benchmarked. For example, if an investor creates a portfolio of 80 stocks that he is benchmarking against NASDAQ 100, then his beta will represent how his portfolio of 80 stocks is performing against the benchmark NASDAQ 100 Index. If Mary creates a portfolio of 400 stocks and benchmarks it against S&P 500, her portfolio beta will represent how it is performing against S&P 500 Index.

The beta is calculated using regression analysis. (Investopedia provides two detailed articles on how beta can be calculated – Calculating Beta: Portfolio Math for Average Investor and How to calculate Beta in Excel?)

**Interpreting Beta**

If the beta of a portfolio comes to one against its benchmark (like a market index), it indicates that portfolio performance and volatility will closely mirror the performance and volatility of benchmark index. A 2% up move or 3% down move in an index should result in similar 2% up move or 3% down in the portfolio.

If beta of a portfolio is 1.3, then portfolio is expected to be 30% more volatile in either direction than the benchmark. If beta is 0.5, then portfolio is half as volatile as the market. A 20% up/down move in the market index will mean portfolio moving 10% up/down respectively.

The following section begins with simplest example of a standard index-based portfolio, followed by more variants of complex portfolios. Each describes how using futures can help reduce risk.

In each case, assume that the investor is aware of a potential decline due to an expected interest rate increase, but he does not want to sell the securities in his portfolio for reasons like tax benefits, dividend eligibility, or long-term holding.

**Scenario 1**

Index-based investments have gained momentum in the last decade, as is evident from continually increasing investment amounts in index-based products like the exchange traded funds (ETFs) and index funds. An investor can hold a diversified portfolio of stocks similar to that of a popular index like the S&P 500, the Russell 2000, or the NASDAQ 100 Index, or he may simply be holding an ETF or an index fund which replicates his selected index. In essence, his portfolio is mirrors the index (beta value = 1), but is not free from the systematic risk. Let’s examine how this market risk can be reduced.

Since the portfolio exactly replicates the benchmark index, one can simply buy an appropriate number of NASDAQ 100 futures contracts to avoid the market risk.

The contract value of NASDAQ 100 futures is $100 times the index value. Assume that the portfolio value is $270,000 and NASDAQ 100 June 2015 futures is trading at $4,400. The number of futures contracts to short sell = ($270,000)/($100* 4,400) = 0.613 contracts.

Since it may not be possible to short sell fractional contracts, the e-mini NASDAQ 100 contracts can be considered, which offer a lower contract size of $20 * NASDAQ 100 index. The number of e-mini contracts to short sell = ($270,000)/($20 * 4,400) = 3.06 or approximately 3 e-mini contracts.

How will this protect the portfolio? The addition of short futures to the portfolio will effectively neutralize the gain or loss due to price fluctuations. Let’s assume the portfolio value goes down from $270,000 to $200,000, leaving a loss of $70,000 (approximately 25.93% loss). The short futures position will become profitable by same proportion, as portfolio beta is one. The NASDAQ 100 futures price will move down approximately 26%, from earlier $4,400 to $3,256, enabling the investor to profit on short position by the differential of $1,144. Since he is holding three mini contracts, each worth $20 times, the overall profit on short futures will be $1,144*3*$20 = $68,640 approximately. This will almost fully nullify his $70,000 loss on portfolio. Using the short futures position, the investor was able to hedge the portfolio risk to a large extent, with fractional loss residual.

The short futures position requires margin money to be maintained. If the NASDAQ 100 starts to climb up, then more margin money will be required. Overall, it will vary during the holding period.

Similar protection can be achieved by buying a long put option to cover for the portfolio value. Instead of varying the margin money requirement for short futures position, one can pay a one-time cost to buy put options for similar protection. In the above scenario, buying three mini-Nasdaq 100 put options with a strike price of $4,400 at $180 each will provide the same protection. Total cost =$180*3 = $540. Assuming the same decline of approximately 26%, the buyer (portfolio holder) will be eligible for payout of (strike price – current underlying) = ($4,400 - $3,256) = $1,144. Since he is holding three mini options each worth $20 times, the overall payoff from options in scenario of decline will be $1,144*3*$20 = $68,640, which is sufficient to approximately cover the $70,000 loss on his portfolio.

Buying options involves a one-time non-refundable cost of option premium ($180*3 = $540 = fractional cost of portfolio value), but takes away the hassle of margin money requirements for shorting futures.

Now let’s quickly wade through other scenarios and how the calculations will work for each of them.

**Scenario 2: **How to protect a portfolio with beta value not equal to one?

Suppose the portfolio worth $400,000 has a beta value is 0.5 against the benchmark S&P 500 index, which is currently at 2,100. The goal is to hedge this portfolio value against any declines.

Each mini S&P 500 futures contract size currently trading at $2,080 is $50 times the index value. The number of e-mini futures contracts to short sell = ($400,000)/($20 * 2,080) = 3.86 e-mini contracts.

However, the portfolio beta is 0.5, implying that the portfolio varies 50% relative to index performance. The number of contracts will also get adjusted for the beta factor, which will take the number of e-mini futures contract to (3.86 * 0.5 = approximately two mini futures contracts).

In case of a decline in portfolio value from $400,000 to say $360,000 ($40,000 or 10% decline), the benchmark index will ideally decline by 20%, as the beta is 0.5. Such a decline will lead to profit from short futures position as follows:

The futures contract price will also decline around 20%, from $2,080 to $1,664 (differential of $416).), resulting in a payoff of ($416* 2 contracts * $50 times index value) = $41,600 net receivable. This will cover the 10% decline in portfolio value. Due to calculations involving fractional value of beta and futures contract, a perfect hedge may not be possible, but the approximate position is covered.

**Scenario 3: **Partial Hedge

Due to fractional figures in hedging calculations, it may not always be possible to perfectly hedge a portfolio. The example in Scenario 2 is a good representation, but sometimes the protective cover may vary widely (plus or minus by significant amount). Additionally, an investor may not like to go for complete portfolio protection and may be good with a partial protection, say to the tune of 50% of portfolio value. This can happen when an investor is certain about his portfolio value not going beyond a set limit of 50% on the downside, and hence he does not want to spend money and block capital to take large hedging positions. Using calculations similar to those above, divided for a partial hedge, one can buy an appropriate number of contracts.

**Scenario 4: **Progressive Hedge

A variant to a partial hedge, a progressive hedge is initiated by taking futures positions with a fixed factor of a partial hedge (say 50%). Depending on the market developments, the coverage is increased in a pre-determined progressive manner, say increasing the futures position by 10% on a 20% decline of portfolio value, and so on. Similarly, on the reverse trend of price up move, the protective futures position can be gradually squared off in a phased manner.

As mentioned in the first scenario, apart from short futures positions, portfolio protection can also be achieved by buying protective puts. Shorting futures requires margin money to be maintained throughout the duration, while long puts require upfront non-refundable costs without the hassles of varying margin money requirements. In both cases, the purpose is to protect the portfolio value on declines, for a small fractional cost.

**Constraints of Portfolio Protection using futures: **Care should be taken about the different scenarios that can occur during the hedging period.

- The basis of all the above-mentioned strategies is the beta factor. Unfortunately, it varies as time passes by, and can lead to significant impacts to portfolio coverage. Experienced portfolio managers usually follow the progressive hedging by using futures and keeping a close eye on varying factors.
- It may not be possible to get the perfect protection due to approximations and rounding factors in calculations. Sufficient room should be kept for such deficit or surplus.
- Portfolio protection can be accomplished only for a specified time period, usually bound by the futures (and options) expiry. On one hand it allows portfolio managers to update their portfolio hedging, but on the other, it does enforce transactional costs.
- Margin money requirements can vary when shorting futures.

**The Bottom Line**

Using futures (and options) is an efficient way to achieve portfolio hedging for a specified period of time. At a fractional cost compared to portfolio value, an investor can maintain the protection for his portfolio, provided he keeps a close eye on the varying parameters and makes adjustments at frequent intervals.