<?xml version="1.0" encoding="utf-8"?>
<InstanceReport xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema">
  <Version>1.0.0.3</Version>
  <hasSegments>false</hasSegments>
  <ReportName>Derivatives and Hedging</ReportName>
  <RoundingOption />
  <Columns>
    <Column>
      <LabelColumn>false</LabelColumn>
      <Id>1</Id>
      <Labels>
        <Label Id="1" Label="3 Months Ended" />
        <Label Id="2" Label="Jun. 30, 2009" />
        <Label Id="4" Label="USD / shares" />
      </Labels>
      <CurrencySymbol>$</CurrencySymbol>
      <hasSegments>false</hasSegments>
      <hasScenarios>false</hasScenarios>
      <Segments />
      <Scenarios />
      <Units>
        <Unit>
          <UnitID>Shares</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>USD</UnitID>
          <UnitType>Standard</UnitType>
          <StandardMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </StandardMeasure>
          <Scale>0</Scale>
        </Unit>
        <Unit>
          <UnitID>USDPerShare</UnitID>
          <UnitType>Divide</UnitType>
          <NumeratorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/iso4217</MeasureSchema>
            <MeasureValue>USD</MeasureValue>
            <MeasureNamespace>iso4217</MeasureNamespace>
          </NumeratorMeasure>
          <DenominatorMeasure>
            <MeasureSchema>http://www.xbrl.org/2003/instance</MeasureSchema>
            <MeasureValue>shares</MeasureValue>
            <MeasureNamespace>xbrli</MeasureNamespace>
          </DenominatorMeasure>
          <Scale>0</Scale>
        </Unit>
      </Units>
    </Column>
  </Columns>
  <Rows>
    <Row>
      <Id>2</Id>
      <Label>NOTES TO CONSOLIDATED FINANCIAL STATEMENTS</Label>
      <Level>0</Level>
      <ElementName>lm_NotesToConsolidatedFinancialStatementsAbstract</ElementName>
      <ElementPrefix>lm</ElementPrefix>
      <IsBaseElement>false</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ElementDataType>string</ElementDataType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>true</IsAbstractGroupTitle>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsEPS>false</IsEPS>
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText />
          <NonNumericTextHeader />
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
        </Cell>
      </Cells>
      <ElementDefenition>No definition available.</ElementDefenition>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
    <Row>
      <Id>3</Id>
      <Label>Derivatives and Hedging</Label>
      <Level>1</Level>
      <ElementName>us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock</ElementName>
      <ElementPrefix>us-gaap</ElementPrefix>
      <IsBaseElement>true</IsBaseElement>
      <BalanceType>na</BalanceType>
      <PeriodType>duration</PeriodType>
      <ElementDataType>string</ElementDataType>
      <ShortDefinition>No definition available.</ShortDefinition>
      <IsReportTitle>false</IsReportTitle>
      <IsSegmentTitle>false</IsSegmentTitle>
      <IsSubReportEnd>false</IsSubReportEnd>
      <IsCalendarTitle>false</IsCalendarTitle>
      <IsTuple>false</IsTuple>
      <IsAbstractGroupTitle>false</IsAbstractGroupTitle>
      <IsBeginningBalance>false</IsBeginningBalance>
      <IsEndingBalance>false</IsEndingBalance>
      <IsEPS>false</IsEPS>
      <Cells>
        <Cell>
          <Id>1</Id>
          <ShowCurrencySymbol>false</ShowCurrencySymbol>
          <IsNumeric>false</IsNumeric>
          <NumericAmount>0</NumericAmount>
          <RoundedNumericAmount>0</RoundedNumericAmount>
          <NonNumbericText>&lt;!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"&gt;
&lt;HTML&gt;&lt;HEAD&gt;
&lt;META http-equiv=Content-Type content="text/html; charset=utf-8"&gt;
&lt;META content="MSHTML 6.00.2900.3492" name=GENERATOR&gt;&lt;/HEAD&gt;
&lt;BODY&gt;
&lt;P style="FONT-SIZE: 12pt; MARGIN: 0pt; LINE-HEIGHT: 14pt"&gt;&lt;B&gt;12.
&amp;nbsp;Derivatives and Hedging&lt;/B&gt;&lt;/P&gt;
&lt;P style="MARGIN: 0pt"&gt;&lt;BR&gt;&lt;/P&gt;
&lt;P style="FONT-SIZE: 12pt; MARGIN: 0pt; LINE-HEIGHT: 14pt" align=justify&gt;During
the three months ended June 30, 2009, Legg Mason did not hold any derivatives
designated in a formal hedge relationship under SFAS No. 133, &amp;#147;Accounting for
Derivative Instruments and Hedging Activities&amp;#148;.&lt;/P&gt;
&lt;P style="MARGIN: 0pt" align=justify&gt;&lt;BR&gt;&lt;/P&gt;
&lt;P style="FONT-SIZE: 12pt; MARGIN: 0pt; LINE-HEIGHT: 14pt" align=justify&gt;Legg
Mason continues to use currency forwards to economically hedge the risk of
movements in exchange rates, primarily between the U.S. dollar, euro, Great
Britain pounds, Canadian dollars, and Australian dollars. &amp;nbsp;As of June 30,
2009, Legg Mason had open currency forward contracts with aggregate gross fair
values of $3,632 and $2,393, classified as Other assets and Other liabilities,
respectively. &amp;nbsp;In the Consolidated Balance Sheets, Legg Mason nets the fair
value of certain foreign currency forwards executed with the same counterparty
where Legg Mason has both the legal right and intent to settle the contracts on
a net basis. &amp;nbsp;For the quarter ended June 30, 2009, $(3,558) was recognized
in Other income (expense) relating to currency forward contracts intended to
offset actual movements in currency exchange rates.&lt;/P&gt;
&lt;P style="MARGIN: 0pt" align=justify&gt;&lt;BR&gt;&lt;/P&gt;
&lt;P style="FONT-SIZE: 12pt; MARGIN: 0pt; LINE-HEIGHT: 14pt" align=justify&gt;As more
fully described in Note 10, Legg Mason has engaged in various forms of liquidity
fund support transactions that constitute derivatives.&lt;/P&gt;&lt;/BODY&gt;&lt;/HTML&gt;
</NonNumbericText>
          <NonNumericTextHeader>12.
&amp;nbsp;Derivatives and Hedging

During
the three months ended June 30, 2009, Legg Mason did not hold any derivatives
designated in a formal hedge</NonNumericTextHeader>
          <FootnoteIndexer />
          <hasSegments>false</hasSegments>
          <hasScenarios>false</hasScenarios>
        </Cell>
      </Cells>
      <ElementDefenition>No definition available.</ElementDefenition>
      <ElementReferences>No authoritative reference available.</ElementReferences>
      <IsTotalLabel>false</IsTotalLabel>
    </Row>
  </Rows>
  <Footnotes />
  <ComparabilityReport>false</ComparabilityReport>
  <NumberOfCols>1</NumberOfCols>
  <NumberOfRows>2</NumberOfRows>
  <HasScenarios>false</HasScenarios>
  <MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel>
  <SharesRoundingLevel>UnKnown</SharesRoundingLevel>
  <PerShareRoundingLevel>UnKnown</PerShareRoundingLevel>
  <HasPureData>false</HasPureData>
  <SharesShouldBeRounded>true</SharesShouldBeRounded>
</InstanceReport>
