# Hedging a stock Portfolio how to calculate

Hedging a stock Portfolio

We should now redirect our attention to using Nifty futures to hedge a portfolio of stocks. You may be wondering why we should select Nifty futures rather than another option.

It is important to remember that when we have a diversified portfolio, we are naturally lowering unsystematic risk. The only factor left in this scenario is the systematic risk. This can be addressed by using an index, such as Nifty futures, which accurately reflects market conditions and thus insulates against risk.

I have invested Rs.800,000 across a range of stocks. This includes equities in the banking sector, retail companies and energy firms.

Step 1 – Portfolio Beta

Determining the “Portfolio Beta” is the initial step when hedging a stock portfolio.

• Portfolio beta is the aggregate of all the individual stock betas weighted by their respective investment proportion.
• Weighted beta is determined by multiplying the portfolio’s individual stock betas with their respective weightings.
• The amount allocated to each stock is determined by dividing the investment in that particular stock by the total value of the portfolio.
• For example, weightage of Axis Bank is 125,000/800,000 = 15.6%
• Hence the weighted beta of Axis Bank on the portfolio would be 15.6% * 1.4 = 0.21

The sum of the weighted beta gives the overall Portfolio Beta for this portfolio which is 1.223. Therefore if Nifty rises by 1%, it is expected that the portfolio will increase by 1.223% and if Nifty falls then the portfolio would be anticipated to drop by an equivalent amount.

Step 2 – Calculate the hedge value

The total value of a hedge is derived from the Portfolio Beta multiplied by the total investment made in the portfolio.

= 1.223 * 800,000

= 978,400/-

It is crucial to keep in mind that this is a ‘long only’ portfolio, for which the stocks were bought directly from the spot market. We know that hedging involves taking an offsetting position in the futures markets. The hedge value indicates that we need to short futures of Rs.978,400/- in order to hedge a portfolio of Rs.800,000/-. This makes perfect sense because we are dealing with a high-beta portfolio.

Step 3 – Calculate the number of lots required

Nifty futures are currently trading at 9025, and with the lot size being 25, the contract value of each lot comes to –

= 9025 * 25

= Rs.225,625/-

Therefore, to short Nifty Futures one will need to buy a certain amount of lots.

= Hedge Value / Contract Value

= 978,400 / 225625

= 4.33

The calculation above implies that, in order to appropriately hedge a portfolio of Rs.800,000/- with a beta of 1.223, one needs to short either 4 or 5 lots of Nifty futures since fractional lot sizes are not available.

If we opt to short 4 lots, we’ll be slightly under hedged, and if we go for 5 units, we’ll be over hedged. This obstacle hinders our ability to accurately hedge a portfolio.

Let us assume the Nifty drops by 500 points (or about 5.5%), now that we have gone ahead with the hedge. This will enable to measure the efficacy of the portfolio hedge. Just for illustration, let’s say we can short 4.33 lots.

Nifty Position

Short initiated at – 9025

Decline in Value – 500 points

Nifty value – 8525

Number of lots – 4.33

P & L = 4.33 * 25 * 500 = Rs.54,125

The short position has seen a growth of Rs.54,125/-. We will investigate what could have caused this shift in the portfolio.

Portfolio Position

Portfolio Value = Rs.800,000/-

Portfolio Beta = 1.223

Decline in Market = 5.5%

Expected Decline in Portfolio = 5.5% * 1.233 = 6.78%

= 6.78% * 800000

= Rs. 54,240

Altogether, the Nifty futures position has increased by Rs.54,125 and the long portfolio has decreased by Rs.54,240. This creates a zero effect in terms of net change in the market. The negative outcome of the portfolio is counterbalanced with the gains made from the Nifty short position.

I believe you now comprehend how to hedge a portfolio of stocks. To further explore the concept, I suggest changing 4.33 lots to either 4 or 5 and running the exercise again.

Before we conclude this chapter, let us take a look at the two unanswered questions from when we discussed hedging single stock positions. Here they are again –

1. What if I take a position in a stock that doesn’t have a futures contract? Say, South Indian Bank. Is it possible to hedge my spot exposure there?
2. In this example, the spot position value was Rs.570,000/-, but what about positions that are relatively smaller – like Rs.50,000/- or Rs.100,000/-? Is it feasible to hedge these too?

You can use hedging for stocks that do not offer stock futures. Consider you have Rs.500,000/- worth of South Indian Bank. Simply multiply the stock’s beta with its investment value to determine the total hedge value. In this case, assuming the stock has a beta of 0.75, the amount of hedging will be

500000*0.75

= 375,000/-

Once you reach the hedge value, divide it by the Nifty’s contract value to calculate the number of lots you will need to short in the futures market. This will help secure your spot position.

Regarding the second inquiry, while you cannot hedge small positions whose cost is comparatively reduced than the contract worth of Nifty, one can still do so through options. We shall discuss this when we examine options.