<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>010300 - Disclosure - RECENT INVESTMENT ACTIVITY</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

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</LabelSeparator><Level>1</Level><ElementName>sre_NotesToConsolidatedFinancialStatementsAbstract</ElementName><ElementPrefix>sre_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Notes to Consolidated Financial Statements [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>sre_RecentInvestmentActivityTextBlock</ElementName><ElementPrefix>sre_</ElementPrefix><IsBaseElement>false</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="FROM_Apr01_2013_TO_Jun30_2013" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;p style='margin-top:24pt; margin-bottom:6pt'&gt;&lt;font style="font-family:Arial;font-size:11pt;margin-left:0px;"&gt;NOTE 3. &lt;/font&gt;&lt;font style="font-family:Arial;font-size:11pt;"&gt;ACQUISITION AND &lt;/font&gt;&lt;font style="font-family:Arial;font-size:11pt;"&gt;DIVESTITURE&lt;/font&gt;&lt;font style="font-family:Arial;font-size:11pt;"&gt; ACTIVITY&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:0pt; margin-bottom:6pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:0px;"&gt;We discu&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;ss our investments in unconsolidated entities&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; in Note 4&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;.&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top: 0pt; margin-bottom: 0pt;'&gt;&lt;/p&gt;&lt;p style='margin-top:21pt; margin-bottom:6pt'&gt;&lt;font style="font-family:Arial;font-size:10pt;font-weight:bold;margin-left:0px;"&gt;SEMPRA NATURAL GAS&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:12pt; margin-bottom:3pt'&gt;&lt;font style="font-family:Times New Roman;font-size:11pt;font-weight:bold;font-style:italic;margin-left:0px;"&gt;Mesquite Power Sale&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:0pt; margin-bottom:6pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:0px;"&gt;In February 2013, Sempra Natural Gas sold one 625-megawatt (MW) block of its 1,250-MW Mesquite Power natural gas-fired power plant in Arizona&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;, including a portion &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;related to&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; common plant,&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; for approximately $371 million in cash to the Salt River Project Agricultura&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;l Improvement and Power District&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; (SRP)&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;. The asset was classified as held for sale at December 31, 2012 and we recognized a &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;pre&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;tax &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;gain on&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; the&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; sale of $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;7&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;4 million&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;($44 million after-tax) &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;in 2013&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;.&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;In connection with the sale, we entered into a 20-year operations and maintenance agreement with SRP on February 28, 2013, whereby SRP assumes plant operations&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; and maintenance of the facility&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;, including our &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;remaining &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;625-MW&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;block.&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; We provide additional information concerning the operations and maintenance agreement in Note 10.&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:12pt; margin-bottom:3pt'&gt;&lt;font style="font-family:Times New Roman;font-size:11pt;font-weight:bold;font-style:italic;margin-left:0px;"&gt;Willmut&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:11pt;font-weight:bold;font-style:italic;"&gt; Gas Company&lt;/font&gt;&lt;/p&gt;&lt;p style='margin-top:0pt; margin-bottom:6pt'&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;margin-left:0px;"&gt;In May 2012, Sempra Natural Gas acquired &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;100 percent of the outstanding common stock of &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;Willmut&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; Gas, a regulated natural gas distribution utility &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;serving approximately 20,000 customers&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; in Hattiesburg, Mississippi, for $19 million in cash and the assumption of &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;$10&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; million of liabilities&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;. &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;Pro forma impacts on revenues and earnings for Sempra Energy had the acquisition occurred on January 1, 2011 were additional revenues of $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;7&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; million and &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;negligible&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; earnings for the &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;six&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; months ended &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;June&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; &lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;30&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;, 2012&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; and additional revenues of $&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt;1&lt;/font&gt;&lt;font style="font-family:Times New Roman;font-size:10pt;"&gt; million and negligible earnings for the three months ended June 30, 2012.&lt;/font&gt;&lt;/p&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>No authoritative reference available.</ElementDefenition><ElementReferences>No definition available.</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Recent Investment Activity</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>RECENT INVESTMENT ACTIVITY</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.sempra.com/role/DisclosureRECENTINVESTMENTACTIVITY</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
