Calculate the Sharpe-maximising portfolio for a given volatility (i.e max return
        for a target risk).

        :param target_risk: the desired volatility of the resulting portfolio.
        :type target_risk: float
        :param risk_free_rate: risk-free rate of borrowing/lending, defaults to 0.02
        :type risk_free_rate: float, optional
        :param market_neutral: whether the portfolio should be market neutral (weights sum to zero),
                               defaults to False. Requires negative lower weight bound.
        :param market_neutral: bool, optional
        :raises ValueError: if ``target_risk`` is not a positive float
        :raises ValueError: if ``risk_free_rate`` is non-numeric
        :return: asset weights for the efficient risk portfolio
        :rtype: dict

def efficient_risk(self, target_risk, risk_free_rate=0.02, market_neutral=False):
        """
        Calculate the Sharpe-maximising portfolio for a given volatility (i.e max return
        for a target risk).

        :param target_risk: the desired volatility of the resulting portfolio.
        :type target_risk: float
        :param risk_free_rate: risk-free rate of borrowing/lending, defaults to 0.02
        :type risk_free_rate: float, optional
        :param market_neutral: whether the portfolio should be market neutral (weights sum to zero),
                               defaults to False. Requires negative lower weight bound.
        :param market_neutral: bool, optional
        :raises ValueError: if ``target_risk`` is not a positive float
        :raises ValueError: if ``risk_free_rate`` is non-numeric
        :return: asset weights for the efficient risk portfolio
        :rtype: dict
        """
        if not isinstance(target_risk, float) or target_risk < 0:
            raise ValueError("target_risk should be a positive float")
        if not isinstance(risk_free_rate, (int, float)):
            raise ValueError("risk_free_rate should be numeric")

        args = (self.expected_returns, self.cov_matrix, self.gamma, risk_free_rate)
        target_constraint = {
            "type": "ineq",
            "fun": lambda w: target_risk
            - np.sqrt(objective_functions.volatility(w, self.cov_matrix)),
        }
        # The equality constraint is either "weights sum to 1" (default), or
        # "weights sum to 0" (market neutral).
        if market_neutral:
            if self.bounds[0][0] is not None and self.bounds[0][0] >= 0:
                warnings.warn(
                    "Market neutrality requires shorting - bounds have been amended",
                    RuntimeWarning,
                )
                self.bounds = self._make_valid_bounds((-1, 1))
            constraints = [
                {"type": "eq", "fun": lambda x: np.sum(x)},
                target_constraint,
            ]
        else:
            constraints = self.constraints + [target_constraint]

        result = sco.minimize(
            objective_functions.negative_sharpe,
            x0=self.initial_guess,
            args=args,
            method="SLSQP",
            bounds=self.bounds,
            constraints=constraints,
        )
        self.weights = result["x"]
        return dict(zip(self.tickers, self.weights))