Rebalancing a Portfolio

Importance of Portfolio Rebalancing

In this article, we invested Rs.50,000 in a portfolio of banking stocks. The total amount was allocated amongst the 5 stocks in equal proportion. However since fractional shares cannot be bought, the portfolio weight was a close approximation of the equal weighted portfolio that we wanted to create.

Suppose we revisit the portfolio after a year, the market value of each security within the portfolio will most likely be different, thereby affecting the weightage of the security within the portfolio.

Portfolio summary at the end of year 1:

Stock	Number of Shares	Day 0			End of Year 1
		Market Price	Net Worth	Weight of Stocks	Market Price	Net Worth	Weight of Stocks
SBI	61	164.70	10,043.70	20.10%	205.80	12,554.60	20.70%
PNB	131	76.20	9,975.70	19.90%	54.80	7,182.50	11.80%
BOB	72	139.60	10,051.20	20.10%	150.10	10,805.00	17.80%
BOI	114	87.40	9,963.60	19.90%	166.10	18,930.80	31.20%
ALBK	227	44.20	10,022.10	20.00%	49.40	11,224.70	18.50%
Total			50,056.20			60,697.60
Annual Returns						21.30%

In the case of our imaginary portfolio both PNB and BOI saw exaggerated price movements which resulted in drastic change in their weightage within the portfolio.

One option that we have in this case is to ignore the change in weightage and continue to hold the same number of shares. This strategy will allow an investor to earn good returns only if BOI continues to perform well and PNB continues to perform poorly.

Suppose the investor decides to retain the portfolio weights hoping that BOI and PNB will continue to perform in line with their historical performance. In case of the below example, share price of both BOI and PNB increased during the year. While share price increase is always good news, in this case the portfolio was less affected by the 40% increase in price of PNB and more affected by the only 5% increase in share price of BOI. This was because of the respective weights of the scrip’s within the portfolio.

Stock	Number of Shares	End of Year 1			End of Year 2
		Market Price	Net Worth	Weight of Stocks	Market Price	Net Worth	Weight of Stocks
SBI	61	205.80	12,554.60	20.70%	226.40	13,810.00	20.80%
PNB	131	54.80	7,182.50	11.80%	76.80	10,055.50	15.20%
BOB	72	150.10	10,805.00	17.80%	172.60	12,425.80	18.80%
BOI	114	166.10	18,930.80	31.20%	174.40	19,877.40	30.00%
ALBK	227	49.40	11,224.70	18.50%	44.50	10,102.20	15.20%
Total			60,697.60	100%		66,270.90	100%
Annual Returns			21.30%			9.2

Hence it is very important to rebalance.

Rebalancing is a form of risk management that will improve the investors risk-adjusted returns over time.

It involves buying and selling a portion of one’s portfolio in order to set the weight of each scrip back to its original state. If an investor fails to rebalance, the more volatile scrip’s in the portfolio will tend to take over and increase portfolio risk.

Assuming the investor chooses the smarter option of rebalancing at the end of year 1, he will have to buy or sell the shares in this order to ensure that the portfolio remains equal weighted.

Stock	Bought on Day 0	Position after rebalancing	Buy (/Sell)
SBI	61	59	-2
PNB	131	220	89
BOB	72	80	8
BOI	114	75	-39
ALBK	227	243	16

As can be seen the investor bought 89 shares of PNB to make up for the lost weightage and sold 39 shares of BOI to reduce its weightage within the portfolio. Minor adjustments were made in case of other shares as well.

Stock	Number of Shares	End of Year 1			End of Year 2
		Market Price	Net Worth	Weight of Stocks	Number of Shares	Market Price	Net Worth	Weight of Stocks
SBI	61	205.80	12,554.60	20.70%	59	226.40	13,357.20	19.70%
PNB	131	54.80	7,182.50	11.80%	220	76.80	16,887.00	24.90%
BOB	72	150.10	10,805.00	17.80%	80	172.60	13,806.40	20.30%
BOI	114	166.10	18,930.80	31.20%	75	174.40	13,077.20	19.20%
ALBK	227	49.40	11,224.70	18.50%	243	44.50	10,814.30	15.90%
Total			60,697.60	100%			67,942.20	100%
Annual Returns			21.30%				11.90%

Rebalancing allowed the investor to earn a return of 11.9% on his portfolio, a 2.7% (11.9 – 9.2) improvement compared to him when he had not rebalanced. This is because he now has more exposure to PNB whose prices increased significantly during the year and less exposure to BOI whose price moved by only 5%.

Nobody can predict with certainty the future returns of a security, past performance is almost never an indication of future performance.

By trimming back on winners and buying laggards, an investor is not only “buying low and selling high”, a sure shot way to make money, but also reaping the full benefit of diversification.

By giving up on past gainers the investor is accepting limited upside potential for greater investment security.

Now that we have learnt why portfolios should be rebalanced, lets look at when and how rebalancing should be done.

When & How to Rebalance?

There are 3 basic strategies one can adopt to decide when to rebalance a portfolio:

1. Time-only rebalancing strategy : In this case, portfolio is rebalanced at regular intervals like quarterly, semi-annually or yearly. Regardless of how much or how little weights of constituents within a portfolio drift from their target, rebalancing will be done only at a pre determined time. Determining the frequency of rebalancing depends mainly on how much risk an investor wants to take, an investor who wants to avoid risk will rebalance more and vice versa.
2. Threshold-only strategy : This strategy involves rebalancing the weights of the portfolio only if they drift away from the weights set on day 0 by a predetermined margin, like 2%, 5% or 10%. The frequency of rebalancing is irrelevant and might happen as regularly as once every month or once every 3 years.
3. Time and threshold : Portfolio will be rebalanced on a scheduled basis (monthly, quarterly or annually) only if its weight has drifted away from the weight set on day 0 by a predetermined minimum rebalancing margin, such as 2%, 5%, or 10%. If at the time of rebalancing, the portfolio’s weights have deviated by less than the predetermined margin the portfolio will not be rebalanced. If the portfolio’s weights drifts by more than the minimum margin at an intermediate time period, the portfolio will then not be rebalanced.

Now let’s understand the process of how a portfolio should be rebalanced.

STEP 1: Recording target portfolio mix and target rebalancing schedule

When purchasing the scrip’s, record the total cost of each security and the total cost of the portfolio. Number of shares bought will be contingent on the desired portfolio weight of each security. First decide on the rebalancing strategy to be adopted, time and threshold strategy is comprehensive and is the recommended strategy. For illustration purpose let’s assume a margin of 10%, i.e if the weights change by more than 10% portfolio will be rebalanced. The period of rebalance will be quarterly. So if the weights change by more than 10% during a quarter, the weights will be rebalanced at the end of the quarter.

Here’s a sample equi-weighted portfolio:

Stock	Day 0
	Number of shares	Market Price	Net Worth	Weight of Stocks
SBI	61	164.70	10,043.70	20.10%
PNB	131	76.20	9,975.70	19.90%
BOB	72	139.60	10,051.20	20.10%
BOI	114	87.40	9,963.60	19.9%
ALBK	227	44.20	10,022.10	20.0%
Total			50,056.20	100%

STEP 2: Compare the actual weight with the target weight after 3 months

Stock	Day 0				End of Q1			Target Weights
	Number of shares	Market Price	Net Worth	Weight of Stocks	Market Price	Net Worth	Weight of Stocks	Low Limit	High Limit	Rebalancing Required?
SBI	61	164.70	10,043.70	20.10%	214.0	13,056.70	24.9%	10.1%	30.1%	No
PNB	131	76.20	9,975.70	19.90%	72.3	9,476.90	18.1%	9.9%	29.9%	No
BOB	72	139.60	10,051.20	20.10%	148.0	10,654.30	20.3%	10.1%	30.1%	No
BOI	114	87.40	9,963.60	19.9%	97.9	11,159.20	21.3%	9.9%	29.9%	No
ALBK	227	44.20	10,022.10	20.0%	35.3	8,017.60	15.3%	10.0%	30.0%	No
Total			50,056.20	100%		52364.80	100%

At the end of 1st quarter no rebalancing action is required, though weights of shares have moved, they are within the margin.

Lets analyze the same portfolio 3 months later:

Stock	Day 0				End of Q2			Target Weights
	Number of shares	Market Price	Net Worth	Weight of Stocks	Market Price	Net Worth	Weight of Stocks	Low Limit	High Limit
SBI	61	164.70	10,043.70	20.10%	312.80	19,082.90	30.8%	10.1%	30.1%
PNB	131	76.20	9,975.70	19.90%	83.80	10,973.20	17.7%	9.9%	29.9%
BOB	72	139.60	10,051.20	20.10%	195.40	14,071.70	22.7%	10.1%	30.1%
BOI	114	87.40	9,963.60	19.9%	120.60	13,749.80	22.2%	9.9%	29.9%
ALBK	227	44.20	10,022.10	20.0%	17.70	4,008.80	6.5%	10.0%	30.0%
Total			50,056.20	100%		52364.80	100%

We can see that SBI and Allahabad Bank have breached the 10% margin and hence the portfolio will have to be rebalanced.

STEP 3: Buy and/or sell shares to rebalance

The number of shares to be bought or sold is as below:

Stock	Bought on Day 0	Position after rebalancing	Buy (/Sell)
SBI	61	33	-28
PNB	131	122	-9
BOB	72	53	-19
BOI	114	85	-29
ALBK	227	584	357

Rebalancing allows us to reap the full benefit of diversification and hence should be carried out regularly.