SIP vs. Fixed Deposit (FD): Volatility vs. Guarantees

Quantitative Yield Analysis: Systematic Equity Accumulation vs. Fixed-Income FDs

We compare the expected yield structures of equity Systematic Investment Plans (SIP) and bank Fixed Deposits (FD) by analyzing risk premiums, compounding dynamics, and tax-slippage drag.

Mathematical Yield Formulations

Let $r_{\text{fd}}$ be the guaranteed quarterly compounded FD interest rate, and $r_{\text{eq}}$ be the stochastic return rate of the equity asset class.

The final value of an FD corpus over $t$ years with initial capital $P_0$ is:

$$FV_{\text{FD}} = P_0 \times \left(1 + \frac{r_{\text{fd}}}{4}\right)^{4t} \times (1 - \text{Slab Tax Drag})$$

The expected future value of a monthly SIP over $n$ months is:

$$E(FV_{\text{SIP}}) = P \times \sum_{k=1}^{n} (1 + E(i_{\text{eq}}))^k$$

Where $E(i_{\text{eq}})$ is the expected monthly equity rate. Equity investments require factoring in a risk premium ($RP$) over the risk-free rate ($R_f$):

$$E(r_{\text{eq}}) = R_f + RP$$

Tax Slippage Impact

Fixed deposits suffer from annual tax realization (accrual taxation), whereas mutual funds benefit from deferred taxation (realization taxation). The deferred tax structure of mutual funds allows the tax liability portion to remain compounded in the market until redemption, boosting the compound annual yield.