June is typically a weak month for the S&P/ASX 200 Index (ASX: XJO) with its 10-year chart showing a consistent pull back between May and June. Despite posting its best monthly performance for May since 2005 — a rise of 3.5% over the period — certain factors could mean our market will return to its underperforming ways in June.

Accordingly, I believe Australia and New Zealand Banking Group (ASX: ANZ) and Telstra Corporation Ltd (ASX: TLS) are two stocks to keep an eye on in case of a market-wide sell-off.

Why the underperformance?

The Australian share market generally underperforms in June because of tax time. For most individuals, superannuation funds and companies, the cut-off date to calculate their annual income tax liability is 30 June each year.

The share market tends to underperform during this period as investors lock in capital gains or realise capital losses going into the end of financial year. Whilst the motives for selling can be varied (e.g. to fund upcoming tax liabilities or minimise capital gains tax), the result is that the Australian share market experiences a lot of selling over this period causing underperformance.

The flipside

In the past, the share market bounces back during July and August as companies announce reports and most stocks, including Commonwealth Bank of Australia (ASX: CBA), declare their dividends.  The result is generally a rally in stocks.

Accordingly, investors with knowledge of this trend should take advantage of price weaknesses and buy shares in top-notch companies if they fall during June. Here are two blue-chips I’ll be keeping an eye on in June.

ANZ Bank

ANZ shares rallied after announcing half-year results at the start of May, buoyed by management’s initiatives to restructure the bank. The dividend yield sits at approximately 6.4% fully-franked at current prices, which is better than peers CBA and Westpac Banking Corp (ASX:WBC).

I believe this makes the current share price fair value for Australia’s third-largest bank (by market capitalisation), however further weakness could represent a good buying opportunity for the long-term investor.

Telstra Corporation

Telstra’s shares have dropped almost 5% since posting a six-month high in mid-May. The fall takes its coveted semi-annual 15.5 cent dividend to a trailing annualised yield of 5.6%, fully-franked. If the stock falls further, this yield will increase.

With management expected to announce a capital management strategy when it reports in August, it is likely that any price weakness will be temporary making for good buying if the opportunity presents itself.

Foolish takeaway

Long-term investments should not be made on short term trends. The key to successful investing is buying quality companies at fair prices and holding them forever. As such, a few cents up or down should never be cause for concern when the intention is to hold shares in solidly run companies for the long-run.

Nevertheless, wise investing involves taking advantage of market opportunities when they present themselves. As history suggests the share market may fall over June it is prudent to keep a few names like ANZ Bank and Telstra on your shopping list to capitalise on any market weakness.

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Motley Fool contributor Rachit Dudhwala owns shares of Telstra Limited. The Motley Fool Australia has no position in any of the stocks mentioned. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy. This article contains general investment advice only (under AFSL 400691). Authorised by Bruce Jackson.